---
_id: '35644'
author:
- first_name: Martin
  full_name: Kolb, Martin
  id: '48880'
  last_name: Kolb
- first_name: Alexander
  full_name: Klump, Alexander
  id: '45067'
  last_name: Klump
citation:
  ama: Kolb M, Klump A. Uniqueness of the Inverse First Passage Time Problem and the
    Shape of the Shiryaev boundary. <i>Theory of Probability and its Applications</i>.
    2022;67(4):717-744.
  apa: Kolb, M., &#38; Klump, A. (2022). Uniqueness of the Inverse First Passage Time
    Problem and the Shape of the Shiryaev boundary. <i>Theory of Probability and Its
    Applications</i>, <i>67</i>(4), 717–744.
  bibtex: '@article{Kolb_Klump_2022, title={Uniqueness of the Inverse First Passage
    Time Problem and the Shape of the Shiryaev boundary}, volume={67}, number={4},
    journal={Theory of Probability and its Applications}, publisher={Society for Industrial
    and Applied Mathematics}, author={Kolb, Martin and Klump, Alexander}, year={2022},
    pages={717–744} }'
  chicago: 'Kolb, Martin, and Alexander Klump. “Uniqueness of the Inverse First Passage
    Time Problem and the Shape of the Shiryaev Boundary.” <i>Theory of Probability
    and Its Applications</i> 67, no. 4 (2022): 717–44.'
  ieee: M. Kolb and A. Klump, “Uniqueness of the Inverse First Passage Time Problem
    and the Shape of the Shiryaev boundary,” <i>Theory of Probability and its Applications</i>,
    vol. 67, no. 4, pp. 717–744, 2022.
  mla: Kolb, Martin, and Alexander Klump. “Uniqueness of the Inverse First Passage
    Time Problem and the Shape of the Shiryaev Boundary.” <i>Theory of Probability
    and Its Applications</i>, vol. 67, no. 4, Society for Industrial and Applied Mathematics,
    2022, pp. 717–44.
  short: M. Kolb, A. Klump, Theory of Probability and Its Applications 67 (2022) 717–744.
date_created: 2023-01-10T08:13:17Z
date_updated: 2023-01-10T08:13:30Z
department:
- _id: '96'
intvolume: '        67'
issue: '4'
language:
- iso: eng
page: 717-744
publication: Theory of Probability and its Applications
publication_status: published
publisher: Society for Industrial and Applied Mathematics
status: public
title: Uniqueness of the Inverse First Passage Time Problem and the Shape of the Shiryaev
  boundary
type: journal_article
user_id: '85821'
volume: 67
year: '2022'
...
---
_id: '35649'
abstract:
- lang: eng
  text: Motivated by the work [6] of Mariusz Bieniek, Krzysztof Burdzy and Soumik
    Pal we study a Fleming-Viot-type particle system consisting of independently moving
    particles each driven by generalized Bessel processes on the positive real line.
    Upon hitting the boundary {0} this particle is killed and an uniformly chosen
    different one branches into two particles. Using the symmetry of the model and
    the self similarity property of Bessel processes, we obtain a criterion to decide
    whether the particles converge to the origin at a finite time. This addresses
    open problem 1.4 in [6]. Specifically, inspired by [6, Open Problem 1.5], we investigate
    the case of three moving particles and refine the general result of [6, Theorem
    1.1(ii)] extending the regime of drift parameters, where convergence does not
    occur – even to values, where it does occur when considering the case of only
    two particles.
author:
- first_name: Martin
  full_name: Kolb, Martin
  id: '48880'
  last_name: Kolb
- first_name: Matthias
  full_name: Liesenfeld, Matthias
  last_name: Liesenfeld
citation:
  ama: Kolb M, Liesenfeld M. On non-extinction in a Fleming-Viot-type particle model
    with Bessel drift. <i>Electronic Journal of Probability</i>. 2022;(27):1-28. doi:<a
    href="https://doi.org/10.1214/22-EJP866">https://doi.org/10.1214/22-EJP866</a>
  apa: Kolb, M., &#38; Liesenfeld, M. (2022). On non-extinction in a Fleming-Viot-type
    particle model with Bessel drift. <i>Electronic Journal of Probability</i>, <i>27</i>,
    1–28. <a href="https://doi.org/10.1214/22-EJP866">https://doi.org/10.1214/22-EJP866</a>
  bibtex: '@article{Kolb_Liesenfeld_2022, title={On non-extinction in a Fleming-Viot-type
    particle model with Bessel drift}, DOI={<a href="https://doi.org/10.1214/22-EJP866">https://doi.org/10.1214/22-EJP866</a>},
    number={27}, journal={Electronic Journal of Probability}, publisher={Institute
    of Mathematical Statistics}, author={Kolb, Martin and Liesenfeld, Matthias}, year={2022},
    pages={1–28} }'
  chicago: 'Kolb, Martin, and Matthias Liesenfeld. “On Non-Extinction in a Fleming-Viot-Type
    Particle Model with Bessel Drift.” <i>Electronic Journal of Probability</i>, no.
    27 (2022): 1–28. <a href="https://doi.org/10.1214/22-EJP866">https://doi.org/10.1214/22-EJP866</a>.'
  ieee: 'M. Kolb and M. Liesenfeld, “On non-extinction in a Fleming-Viot-type particle
    model with Bessel drift,” <i>Electronic Journal of Probability</i>, no. 27, pp.
    1–28, 2022, doi: <a href="https://doi.org/10.1214/22-EJP866">https://doi.org/10.1214/22-EJP866</a>.'
  mla: Kolb, Martin, and Matthias Liesenfeld. “On Non-Extinction in a Fleming-Viot-Type
    Particle Model with Bessel Drift.” <i>Electronic Journal of Probability</i>, no.
    27, Institute of Mathematical Statistics, 2022, pp. 1–28, doi:<a href="https://doi.org/10.1214/22-EJP866">https://doi.org/10.1214/22-EJP866</a>.
  short: M. Kolb, M. Liesenfeld, Electronic Journal of Probability (2022) 1–28.
date_created: 2023-01-10T08:19:25Z
date_updated: 2023-01-10T08:19:38Z
department:
- _id: '96'
doi: https://doi.org/10.1214/22-EJP866
issue: '27'
language:
- iso: eng
page: 1-28
publication: Electronic Journal of Probability
publication_status: published
publisher: Institute of Mathematical Statistics
status: public
title: On non-extinction in a Fleming-Viot-type particle model with Bessel drift
type: journal_article
user_id: '85821'
year: '2022'
...
---
_id: '35650'
abstract:
- lang: eng
  text: "We consider autoregressive sequences Xn = aXn−1 + ξn and\r\nMn = max{aMn−1
    , ξn} with a constant a ∈ (0, 1) and with positive, in-\r\ndependent and identically
    distributed innovations {ξk }. It is known that if\r\nP(ξ1 > x) ∼ d\r\nlog x with
    some d ∈ (0, − log a) then the chains {Xn} and {Mn}\r\nare null recurrent. We
    investigate the tail behaviour of recurrence times in this\r\ncase of logarithmically
    decaying tails. More precisely, we show that the tails\r\nof recurrence times
    are regularly varying of index −1 − d/ log a. We also prove\r\nlimit theorems
    for {Xn} and {Mn} conditioned to stay over a fixed level x0.\r\nFurthermore, we
    study tail asymptotics for recurrence times of {Xn} and {Mn}\r\nin the case when
    these chains are positive recurrent and the tail of log ξ1 is\r\nsubexponential."
author:
- first_name: Denis
  full_name: Denisov, Denis
  last_name: Denisov
- first_name: Günter
  full_name: Hinrichs, Günter
  last_name: Hinrichs
- first_name: Martin
  full_name: Kolb, Martin
  id: '48880'
  last_name: Kolb
- first_name: Vitali
  full_name: Wachtel, Vitali
  last_name: Wachtel
citation:
  ama: Denisov D, Hinrichs G, Kolb M, Wachtel V. Persistence of autoregressive sequences
    with logarithmic tails. <i>Electronic Journal of Probability</i>. 2022;27:1-43.
    doi:<a href="https://doi.org/10.48550/arXiv.2203.14772">https://doi.org/10.48550/arXiv.2203.14772</a>
  apa: Denisov, D., Hinrichs, G., Kolb, M., &#38; Wachtel, V. (2022). Persistence
    of autoregressive sequences with logarithmic tails. <i>Electronic Journal of Probability</i>,
    <i>27</i>, 1–43. <a href="https://doi.org/10.48550/arXiv.2203.14772">https://doi.org/10.48550/arXiv.2203.14772</a>
  bibtex: '@article{Denisov_Hinrichs_Kolb_Wachtel_2022, title={Persistence of autoregressive
    sequences with logarithmic tails}, volume={27}, DOI={<a href="https://doi.org/10.48550/arXiv.2203.14772">https://doi.org/10.48550/arXiv.2203.14772</a>},
    journal={Electronic Journal of Probability}, publisher={Institute of Mathematical
    Statistics}, author={Denisov, Denis and Hinrichs, Günter and Kolb, Martin and
    Wachtel, Vitali}, year={2022}, pages={1–43} }'
  chicago: 'Denisov, Denis, Günter Hinrichs, Martin Kolb, and Vitali Wachtel. “Persistence
    of Autoregressive Sequences with Logarithmic Tails.” <i>Electronic Journal of
    Probability</i> 27 (2022): 1–43. <a href="https://doi.org/10.48550/arXiv.2203.14772">https://doi.org/10.48550/arXiv.2203.14772</a>.'
  ieee: 'D. Denisov, G. Hinrichs, M. Kolb, and V. Wachtel, “Persistence of autoregressive
    sequences with logarithmic tails,” <i>Electronic Journal of Probability</i>, vol.
    27, pp. 1–43, 2022, doi: <a href="https://doi.org/10.48550/arXiv.2203.14772">https://doi.org/10.48550/arXiv.2203.14772</a>.'
  mla: Denisov, Denis, et al. “Persistence of Autoregressive Sequences with Logarithmic
    Tails.” <i>Electronic Journal of Probability</i>, vol. 27, Institute of Mathematical
    Statistics, 2022, pp. 1–43, doi:<a href="https://doi.org/10.48550/arXiv.2203.14772">https://doi.org/10.48550/arXiv.2203.14772</a>.
  short: D. Denisov, G. Hinrichs, M. Kolb, V. Wachtel, Electronic Journal of Probability
    27 (2022) 1–43.
date_created: 2023-01-10T08:28:12Z
date_updated: 2023-01-10T08:29:02Z
department:
- _id: '96'
doi: https://doi.org/10.48550/arXiv.2203.14772
intvolume: '        27'
language:
- iso: eng
page: 1-43
publication: Electronic Journal of Probability
publication_status: published
publisher: Institute of Mathematical Statistics
status: public
title: Persistence of autoregressive sequences with logarithmic tails
type: journal_article
user_id: '85821'
volume: 27
year: '2022'
...
---
_id: '33278'
abstract:
- lang: eng
  text: The kinetic Brownian motion on the sphere bundle of a Riemannian manifold
    M is a stochastic process that models a random perturbation of the geodesic flow.
    If M is an orientable compact constantly curved surface, we show that in the limit
    of infinitely large perturbation the L2-spectrum of the infinitesimal generator
    of a time-rescaled version of the process converges to the Laplace spectrum of
    the base manifold.
author:
- first_name: Martin
  full_name: Kolb, Martin
  id: '48880'
  last_name: Kolb
- first_name: Tobias
  full_name: Weich, Tobias
  last_name: Weich
- first_name: Lasse
  full_name: Wolf, Lasse
  last_name: Wolf
citation:
  ama: Kolb M, Weich T, Wolf L. Spectral Asymptotics for Kinetic Brownian Motion on
    Surfaces of Constant Curvature. <i>Annales Henri Poincaré </i>. 2021;23(4):1283-1296.
  apa: Kolb, M., Weich, T., &#38; Wolf, L. (2021). Spectral Asymptotics for Kinetic
    Brownian Motion on Surfaces of Constant Curvature. <i>Annales Henri Poincaré </i>,
    <i>23</i>(4), 1283–1296.
  bibtex: '@article{Kolb_Weich_Wolf_2021, title={Spectral Asymptotics for Kinetic
    Brownian Motion on Surfaces of Constant Curvature}, volume={23}, number={4}, journal={Annales
    Henri Poincaré }, publisher={Springer Science + Business Media}, author={Kolb,
    Martin and Weich, Tobias and Wolf, Lasse}, year={2021}, pages={1283–1296} }'
  chicago: 'Kolb, Martin, Tobias Weich, and Lasse Wolf. “Spectral Asymptotics for
    Kinetic Brownian Motion on Surfaces of Constant Curvature.” <i>Annales Henri Poincaré
    </i> 23, no. 4 (2021): 1283–96.'
  ieee: M. Kolb, T. Weich, and L. Wolf, “Spectral Asymptotics for Kinetic Brownian
    Motion on Surfaces of Constant Curvature,” <i>Annales Henri Poincaré </i>, vol.
    23, no. 4, pp. 1283–1296, 2021.
  mla: Kolb, Martin, et al. “Spectral Asymptotics for Kinetic Brownian Motion on Surfaces
    of Constant Curvature.” <i>Annales Henri Poincaré </i>, vol. 23, no. 4, Springer
    Science + Business Media, 2021, pp. 1283–96.
  short: M. Kolb, T. Weich, L. Wolf, Annales Henri Poincaré  23 (2021) 1283–1296.
date_created: 2022-09-07T07:05:33Z
date_updated: 2022-09-08T06:06:13Z
department:
- _id: '96'
intvolume: '        23'
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://link.springer.com/article/10.1007/s00023-021-01121-5
oa: '1'
page: 1283-1296
publication: 'Annales Henri Poincaré '
publication_status: published
publisher: Springer Science + Business Media
related_material:
  link:
  - relation: contains
    url: https://link.springer.com/article/10.1007/s00023-021-01121-5
status: public
title: Spectral Asymptotics for Kinetic Brownian Motion on Surfaces of Constant Curvature
type: journal_article
user_id: '85821'
volume: 23
year: '2021'
...
---
_id: '33481'
abstract:
- lang: eng
  text: While 2D Gibbsian particle systems might exhibit orientational order resulting
    in a lattice-like structure, these particle systems do not exhibit positional
    order if the interaction between particles satisfies some weak assumptions. Here
    we investigate to which extent particles within a box of size may fluctuate from
    their ideal lattice position. We show that particles near the center of the box
    typically show a displacement at least of order . Thus we extend recent results
    on the hard disk model to particle systems with fairly arbitrary particle spins
    and interaction. Our result applies to models such as rather general continuum
    Potts type models, e.g. with Widom–Rowlinson or Lenard-Jones-type interaction.
author:
- first_name: Thomas
  full_name: Richthammer, Thomas
  id: '62054'
  last_name: Richthammer
- first_name: Michael
  full_name: Fiedler, Michael
  last_name: Fiedler
citation:
  ama: Richthammer T, Fiedler M. A lower bound on the displacement of particles in
    2D Gibbsian particle systems. <i>Stochastic Processes and their Applications</i>.
    2021;132:1-32. doi:<a href="https://doi.org/10.1016/j.spa.2020.10.003">https://doi.org/10.1016/j.spa.2020.10.003</a>
  apa: Richthammer, T., &#38; Fiedler, M. (2021). A lower bound on the displacement
    of particles in 2D Gibbsian particle systems. <i>Stochastic Processes and Their
    Applications</i>, <i>132</i>, 1–32. <a href="https://doi.org/10.1016/j.spa.2020.10.003">https://doi.org/10.1016/j.spa.2020.10.003</a>
  bibtex: '@article{Richthammer_Fiedler_2021, title={A lower bound on the displacement
    of particles in 2D Gibbsian particle systems}, volume={132}, DOI={<a href="https://doi.org/10.1016/j.spa.2020.10.003">https://doi.org/10.1016/j.spa.2020.10.003</a>},
    journal={Stochastic Processes and their Applications}, publisher={Elsevier}, author={Richthammer,
    Thomas and Fiedler, Michael}, year={2021}, pages={1–32} }'
  chicago: 'Richthammer, Thomas, and Michael Fiedler. “A Lower Bound on the Displacement
    of Particles in 2D Gibbsian Particle Systems.” <i>Stochastic Processes and Their
    Applications</i> 132 (2021): 1–32. <a href="https://doi.org/10.1016/j.spa.2020.10.003">https://doi.org/10.1016/j.spa.2020.10.003</a>.'
  ieee: 'T. Richthammer and M. Fiedler, “A lower bound on the displacement of particles
    in 2D Gibbsian particle systems,” <i>Stochastic Processes and their Applications</i>,
    vol. 132, pp. 1–32, 2021, doi: <a href="https://doi.org/10.1016/j.spa.2020.10.003">https://doi.org/10.1016/j.spa.2020.10.003</a>.'
  mla: Richthammer, Thomas, and Michael Fiedler. “A Lower Bound on the Displacement
    of Particles in 2D Gibbsian Particle Systems.” <i>Stochastic Processes and Their
    Applications</i>, vol. 132, Elsevier, 2021, pp. 1–32, doi:<a href="https://doi.org/10.1016/j.spa.2020.10.003">https://doi.org/10.1016/j.spa.2020.10.003</a>.
  short: T. Richthammer, M. Fiedler, Stochastic Processes and Their Applications 132
    (2021) 1–32.
date_created: 2022-09-26T06:53:59Z
date_updated: 2022-09-26T06:54:06Z
department:
- _id: '96'
doi: https://doi.org/10.1016/j.spa.2020.10.003
intvolume: '       132'
language:
- iso: eng
page: 1-32
publication: Stochastic Processes and their Applications
publication_status: published
publisher: Elsevier
status: public
title: A lower bound on the displacement of particles in 2D Gibbsian particle systems
type: journal_article
user_id: '85821'
volume: 132
year: '2021'
...
---
_id: '33282'
abstract:
- lang: eng
  text: "We derive a criterium for the almost sure finiteness of perpetual integrals
    of L ́evy\r\nprocesses for a class of real functions including all continuous
    functions and for general one-\r\ndimensional L ́evy processes that drifts to
    plus infinity. This generalizes previous work of D ̈oring\r\nand Kyprianou, who
    considered L ́evy processes having a local time, leaving the general case as an\r\nopen
    problem. It turns out, that the criterium in the general situation simplifies
    significantly in\r\nthe situation, where the process has a local time, but we
    also demonstrate that in general our cri-\r\nterium can not be reduced. This answers
    an open problem posed in D ̈oring, L. and Kyprianou, A.\r\n(2015)."
author:
- first_name: Martin
  full_name: Kolb, Martin
  id: '48880'
  last_name: Kolb
- first_name: Mladen
  full_name: Savov, Mladen
  last_name: Savov
citation:
  ama: Kolb M, Savov M. A Characterization of the Finiteness of Perpetual Integrals
    of Levy Processes. <i>Bernoulli</i>. 2020;26(2):1453-1472. doi:<a href="https://doi.org/10.48550/arXiv.1903.03792">https://doi.org/10.48550/arXiv.1903.03792</a>
  apa: Kolb, M., &#38; Savov, M. (2020). A Characterization of the Finiteness of Perpetual
    Integrals of Levy Processes. <i>Bernoulli</i>, <i>26</i>(2), 1453–1472. <a href="https://doi.org/10.48550/arXiv.1903.03792">https://doi.org/10.48550/arXiv.1903.03792</a>
  bibtex: '@article{Kolb_Savov_2020, title={A Characterization of the Finiteness of
    Perpetual Integrals of Levy Processes}, volume={26}, DOI={<a href="https://doi.org/10.48550/arXiv.1903.03792">https://doi.org/10.48550/arXiv.1903.03792</a>},
    number={2}, journal={Bernoulli}, publisher={Bernoulli Society for Mathematical
    Statistics and Probability}, author={Kolb, Martin and Savov, Mladen}, year={2020},
    pages={1453–1472} }'
  chicago: 'Kolb, Martin, and Mladen Savov. “A Characterization of the Finiteness
    of Perpetual Integrals of Levy Processes.” <i>Bernoulli</i> 26, no. 2 (2020):
    1453–72. <a href="https://doi.org/10.48550/arXiv.1903.03792">https://doi.org/10.48550/arXiv.1903.03792</a>.'
  ieee: 'M. Kolb and M. Savov, “A Characterization of the Finiteness of Perpetual
    Integrals of Levy Processes,” <i>Bernoulli</i>, vol. 26, no. 2, pp. 1453–1472,
    2020, doi: <a href="https://doi.org/10.48550/arXiv.1903.03792">https://doi.org/10.48550/arXiv.1903.03792</a>.'
  mla: Kolb, Martin, and Mladen Savov. “A Characterization of the Finiteness of Perpetual
    Integrals of Levy Processes.” <i>Bernoulli</i>, vol. 26, no. 2, Bernoulli Society
    for Mathematical Statistics and Probability, 2020, pp. 1453–72, doi:<a href="https://doi.org/10.48550/arXiv.1903.03792">https://doi.org/10.48550/arXiv.1903.03792</a>.
  short: M. Kolb, M. Savov, Bernoulli 26 (2020) 1453–1472.
date_created: 2022-09-08T06:36:37Z
date_updated: 2022-09-08T06:48:40Z
department:
- _id: '96'
doi: https://doi.org/10.48550/arXiv.1903.03792
intvolume: '        26'
issue: '2'
keyword:
- L ́evy processes
- Perpetual integrals
- Potential measures
language:
- iso: eng
page: 1453-1472
publication: Bernoulli
publication_status: published
publisher: Bernoulli Society for Mathematical Statistics and Probability
status: public
title: A Characterization of the Finiteness of Perpetual Integrals of Levy Processes
type: journal_article
user_id: '85821'
volume: 26
year: '2020'
...
---
_id: '33330'
abstract:
- lang: eng
  text: 'Reciprocal relations are binary relations Q with entries Q(i,j)∈[0,1], and
    such that Q(i,j)+Q(j,i)=1. Relations of this kind occur quite naturally in various
    domains, such as preference modeling and preference learning. For example, Q(i,j)
    could be the fraction of voters in a population who prefer candidate i to candidate
    j. In the literature, various attempts have been made at generalizing the notion
    of transitivity to reciprocal relations. In this paper, we compare three important
    frameworks of generalized transitivity: g-stochastic transitivity, T-transitivity,
    and cycle-transitivity. To this end, we introduce E-transitivity as an even more
    general notion. We also use this framework to extend an existing hierarchy of
    different types of transitivity. As an illustration, we study transitivity properties
    of probabilities of pairwise preferences, which are induced as marginals of an
    underlying probability distribution on rankings (strict total orders) of a set
    of alternatives. In particular, we analyze the interesting case of the so-called
    Babington Smith model, a parametric family of distributions of that kind.'
author:
- first_name: Björn
  full_name: Haddenhorst, Björn
  last_name: Haddenhorst
- first_name: Eyke
  full_name: Hüllermeier, Eyke
  last_name: Hüllermeier
- first_name: Martin
  full_name: Kolb, Martin
  id: '48880'
  last_name: Kolb
citation:
  ama: 'Haddenhorst B, Hüllermeier E, Kolb M. Generalized transitivity: A systematic
    comparison of concepts with an application to preferences in the Babington Smith
    model. <i>International Journal of Approximate Reasoning</i>. 2020;119(2):373-407.
    doi:<a href="https://doi.org/10.1016/j.ijar.2020.01.007">https://doi.org/10.1016/j.ijar.2020.01.007</a>'
  apa: 'Haddenhorst, B., Hüllermeier, E., &#38; Kolb, M. (2020). Generalized transitivity:
    A systematic comparison of concepts with an application to preferences in the
    Babington Smith model. <i>International Journal of Approximate Reasoning</i>,
    <i>119</i>(2), 373–407. <a href="https://doi.org/10.1016/j.ijar.2020.01.007">https://doi.org/10.1016/j.ijar.2020.01.007</a>'
  bibtex: '@article{Haddenhorst_Hüllermeier_Kolb_2020, title={Generalized transitivity:
    A systematic comparison of concepts with an application to preferences in the
    Babington Smith model}, volume={119}, DOI={<a href="https://doi.org/10.1016/j.ijar.2020.01.007">https://doi.org/10.1016/j.ijar.2020.01.007</a>},
    number={2}, journal={International Journal of Approximate Reasoning}, publisher={Elsevier},
    author={Haddenhorst, Björn and Hüllermeier, Eyke and Kolb, Martin}, year={2020},
    pages={373–407} }'
  chicago: 'Haddenhorst, Björn, Eyke Hüllermeier, and Martin Kolb. “Generalized Transitivity:
    A Systematic Comparison of Concepts with an Application to Preferences in the
    Babington Smith Model.” <i>International Journal of Approximate Reasoning</i>
    119, no. 2 (2020): 373–407. <a href="https://doi.org/10.1016/j.ijar.2020.01.007">https://doi.org/10.1016/j.ijar.2020.01.007</a>.'
  ieee: 'B. Haddenhorst, E. Hüllermeier, and M. Kolb, “Generalized transitivity: A
    systematic comparison of concepts with an application to preferences in the Babington
    Smith model,” <i>International Journal of Approximate Reasoning</i>, vol. 119,
    no. 2, pp. 373–407, 2020, doi: <a href="https://doi.org/10.1016/j.ijar.2020.01.007">https://doi.org/10.1016/j.ijar.2020.01.007</a>.'
  mla: 'Haddenhorst, Björn, et al. “Generalized Transitivity: A Systematic Comparison
    of Concepts with an Application to Preferences in the Babington Smith Model.”
    <i>International Journal of Approximate Reasoning</i>, vol. 119, no. 2, Elsevier,
    2020, pp. 373–407, doi:<a href="https://doi.org/10.1016/j.ijar.2020.01.007">https://doi.org/10.1016/j.ijar.2020.01.007</a>.'
  short: B. Haddenhorst, E. Hüllermeier, M. Kolb, International Journal of Approximate
    Reasoning 119 (2020) 373–407.
date_created: 2022-09-12T07:13:19Z
date_updated: 2022-09-12T07:13:30Z
department:
- _id: '96'
doi: https://doi.org/10.1016/j.ijar.2020.01.007
intvolume: '       119'
issue: '2'
language:
- iso: eng
page: 373-407
publication: International Journal of Approximate Reasoning
publication_status: published
publisher: Elsevier
status: public
title: 'Generalized transitivity: A systematic comparison of concepts with an application
  to preferences in the Babington Smith model'
type: journal_article
user_id: '85821'
volume: 119
year: '2020'
...
---
_id: '33331'
abstract:
- lang: eng
  text: Motivated by the recent contribution (Bauer and Bernard in Annales Henri Poincaré
    19:653–693, 2018), we study the scaling limit behavior of a class of one-dimensional
    stochastic differential equations which has a unique attracting point subject
    to a small additional repulsive perturbation. Problems of this type appear in
    the analysis of continuously monitored quantum systems. We extend the results
    of Bauer and Bernard (Annales Henri Poincaré 19:653–693, 2018) and prove a general
    result concerning the convergence to a homogeneous Poisson process using only
    classical probabilistic tools.
author:
- first_name: Martin
  full_name: Kolb, Martin
  id: '48880'
  last_name: Kolb
- first_name: Matthias
  full_name: Liesenfeld, Matthias
  last_name: Liesenfeld
citation:
  ama: Kolb M, Liesenfeld M. Stochastic Spikes and Poisson Approximation of One-Dimensional
    Stochastic Differential Equations with Applications to Continuously Measured Quantum
    Systems. <i>Annales Henri Poincaré</i>. 2019;20(6):1753-1783. doi:<a href="http://dx.doi.org/10.1007/s00023-019-00772-9">http://dx.doi.org/10.1007/s00023-019-00772-9</a>
  apa: Kolb, M., &#38; Liesenfeld, M. (2019). Stochastic Spikes and Poisson Approximation
    of One-Dimensional Stochastic Differential Equations with Applications to Continuously
    Measured Quantum Systems. <i>Annales Henri Poincaré</i>, <i>20</i>(6), 1753–1783.
    <a href="http://dx.doi.org/10.1007/s00023-019-00772-9">http://dx.doi.org/10.1007/s00023-019-00772-9</a>
  bibtex: '@article{Kolb_Liesenfeld_2019, title={Stochastic Spikes and Poisson Approximation
    of One-Dimensional Stochastic Differential Equations with Applications to Continuously
    Measured Quantum Systems}, volume={20}, DOI={<a href="http://dx.doi.org/10.1007/s00023-019-00772-9">http://dx.doi.org/10.1007/s00023-019-00772-9</a>},
    number={6}, journal={Annales Henri Poincaré}, publisher={Institute Henri Poincaré},
    author={Kolb, Martin and Liesenfeld, Matthias}, year={2019}, pages={1753–1783}
    }'
  chicago: 'Kolb, Martin, and Matthias Liesenfeld. “Stochastic Spikes and Poisson
    Approximation of One-Dimensional Stochastic Differential Equations with Applications
    to Continuously Measured Quantum Systems.” <i>Annales Henri Poincaré</i> 20, no.
    6 (2019): 1753–83. <a href="http://dx.doi.org/10.1007/s00023-019-00772-9">http://dx.doi.org/10.1007/s00023-019-00772-9</a>.'
  ieee: 'M. Kolb and M. Liesenfeld, “Stochastic Spikes and Poisson Approximation of
    One-Dimensional Stochastic Differential Equations with Applications to Continuously
    Measured Quantum Systems,” <i>Annales Henri Poincaré</i>, vol. 20, no. 6, pp.
    1753–1783, 2019, doi: <a href="http://dx.doi.org/10.1007/s00023-019-00772-9">http://dx.doi.org/10.1007/s00023-019-00772-9</a>.'
  mla: Kolb, Martin, and Matthias Liesenfeld. “Stochastic Spikes and Poisson Approximation
    of One-Dimensional Stochastic Differential Equations with Applications to Continuously
    Measured Quantum Systems.” <i>Annales Henri Poincaré</i>, vol. 20, no. 6, Institute
    Henri Poincaré, 2019, pp. 1753–83, doi:<a href="http://dx.doi.org/10.1007/s00023-019-00772-9">http://dx.doi.org/10.1007/s00023-019-00772-9</a>.
  short: M. Kolb, M. Liesenfeld, Annales Henri Poincaré 20 (2019) 1753–1783.
date_created: 2022-09-12T07:18:58Z
date_updated: 2022-09-12T07:19:02Z
department:
- _id: '96'
doi: http://dx.doi.org/10.1007/s00023-019-00772-9
intvolume: '        20'
issue: '6'
language:
- iso: eng
page: 1753-1783
publication: Annales Henri Poincaré
publication_status: published
publisher: Institute Henri Poincaré
status: public
title: Stochastic Spikes and Poisson Approximation of One-Dimensional Stochastic Differential
  Equations with Applications to Continuously Measured Quantum Systems
type: journal_article
user_id: '85821'
volume: 20
year: '2019'
...
---
_id: '33333'
author:
- first_name: Andi Q.
  full_name: Wang, Andi Q.
  last_name: Wang
- first_name: Martin
  full_name: Kolb, Martin
  id: '48880'
  last_name: Kolb
- first_name: Gareth O.
  full_name: Roberts, Gareth O.
  last_name: Roberts
- first_name: David
  full_name: Steinsaltz, David
  last_name: Steinsaltz
citation:
  ama: Wang AQ, Kolb M, Roberts GO, Steinsaltz D. Theoretical properties of quasi-stationary
    Monte Carlo methods. <i>The Annals of Applied Probability</i>. 2019;29(1). doi:<a
    href="http://dx.doi.org/10.1214/18-AAP1422">http://dx.doi.org/10.1214/18-AAP1422</a>
  apa: Wang, A. Q., Kolb, M., Roberts, G. O., &#38; Steinsaltz, D. (2019). Theoretical
    properties of quasi-stationary Monte Carlo methods. <i>The Annals of Applied Probability</i>,
    <i>29</i>(1). <a href="http://dx.doi.org/10.1214/18-AAP1422">http://dx.doi.org/10.1214/18-AAP1422</a>
  bibtex: '@article{Wang_Kolb_Roberts_Steinsaltz_2019, title={Theoretical properties
    of quasi-stationary Monte Carlo methods}, volume={29}, DOI={<a href="http://dx.doi.org/10.1214/18-AAP1422">http://dx.doi.org/10.1214/18-AAP1422</a>},
    number={1}, journal={The Annals of Applied Probability}, author={Wang, Andi Q.
    and Kolb, Martin and Roberts, Gareth O. and Steinsaltz, David}, year={2019} }'
  chicago: Wang, Andi Q., Martin Kolb, Gareth O. Roberts, and David Steinsaltz. “Theoretical
    Properties of Quasi-Stationary Monte Carlo Methods.” <i>The Annals of Applied
    Probability</i> 29, no. 1 (2019). <a href="http://dx.doi.org/10.1214/18-AAP1422">http://dx.doi.org/10.1214/18-AAP1422</a>.
  ieee: 'A. Q. Wang, M. Kolb, G. O. Roberts, and D. Steinsaltz, “Theoretical properties
    of quasi-stationary Monte Carlo methods,” <i>The Annals of Applied Probability</i>,
    vol. 29, no. 1, 2019, doi: <a href="http://dx.doi.org/10.1214/18-AAP1422">http://dx.doi.org/10.1214/18-AAP1422</a>.'
  mla: Wang, Andi Q., et al. “Theoretical Properties of Quasi-Stationary Monte Carlo
    Methods.” <i>The Annals of Applied Probability</i>, vol. 29, no. 1, 2019, doi:<a
    href="http://dx.doi.org/10.1214/18-AAP1422">http://dx.doi.org/10.1214/18-AAP1422</a>.
  short: A.Q. Wang, M. Kolb, G.O. Roberts, D. Steinsaltz, The Annals of Applied Probability
    29 (2019).
date_created: 2022-09-12T07:24:52Z
date_updated: 2022-09-12T07:32:35Z
department:
- _id: '96'
doi: http://dx.doi.org/10.1214/18-AAP1422
intvolume: '        29'
issue: '1'
language:
- iso: eng
publication: The Annals of Applied Probability
status: public
title: Theoretical properties of quasi-stationary Monte Carlo methods
type: journal_article
user_id: '85821'
volume: 29
year: '2019'
...
---
_id: '33334'
abstract:
- lang: eng
  text: In the present work we characterize the existence of quasistationary distributions
    for diffusions on (0,∞) allowing singular behavior at 0 and ∞. If absorption at
    0 is certain, we show that there exists a quasistationary distribution as soon
    as the spectrum of the generator is strictly positive. This complements results
    of Collet et al. and Kolb/Steinsaltz for 0 being a regular boundary point and
    extends results by Collet et al. on singular diffusions. We also study the existence
    and uniqueness of quasistationary distributions for a class of one-dimensional
    diffusions with killing that arise from a biological example and which have two
    inaccessible boundary points (more specifically 0 is natural and ∞ is entrance).
author:
- first_name: Alexandru
  full_name: Hening, Alexandru
  last_name: Hening
- first_name: Martin
  full_name: Kolb, Martin
  last_name: Kolb
citation:
  ama: Hening A, Kolb M. Quasistationary distributions for one-dimensional diffusions
    with two singular boundary points. <i>Stochastic Processes and their Applications</i>.
    2019;129(5):1659-1696. doi:<a href="http://dx.doi.org/10.1016/j.spa.2018.05.012">http://dx.doi.org/10.1016/j.spa.2018.05.012</a>
  apa: Hening, A., &#38; Kolb, M. (2019). Quasistationary distributions for one-dimensional
    diffusions with two singular boundary points. <i>Stochastic Processes and Their
    Applications</i>, <i>129</i>(5), 1659–1696. <a href="http://dx.doi.org/10.1016/j.spa.2018.05.012">http://dx.doi.org/10.1016/j.spa.2018.05.012</a>
  bibtex: '@article{Hening_Kolb_2019, title={Quasistationary distributions for one-dimensional
    diffusions with two singular boundary points}, volume={129}, DOI={<a href="http://dx.doi.org/10.1016/j.spa.2018.05.012">http://dx.doi.org/10.1016/j.spa.2018.05.012</a>},
    number={5}, journal={Stochastic Processes and their Applications}, publisher={Bernoulli
    Society for Mathematical Statistics and Probability}, author={Hening, Alexandru
    and Kolb, Martin}, year={2019}, pages={1659–1696} }'
  chicago: 'Hening, Alexandru, and Martin Kolb. “Quasistationary Distributions for
    One-Dimensional Diffusions with Two Singular Boundary Points.” <i>Stochastic Processes
    and Their Applications</i> 129, no. 5 (2019): 1659–96. <a href="http://dx.doi.org/10.1016/j.spa.2018.05.012">http://dx.doi.org/10.1016/j.spa.2018.05.012</a>.'
  ieee: 'A. Hening and M. Kolb, “Quasistationary distributions for one-dimensional
    diffusions with two singular boundary points,” <i>Stochastic Processes and their
    Applications</i>, vol. 129, no. 5, pp. 1659–1696, 2019, doi: <a href="http://dx.doi.org/10.1016/j.spa.2018.05.012">http://dx.doi.org/10.1016/j.spa.2018.05.012</a>.'
  mla: Hening, Alexandru, and Martin Kolb. “Quasistationary Distributions for One-Dimensional
    Diffusions with Two Singular Boundary Points.” <i>Stochastic Processes and Their
    Applications</i>, vol. 129, no. 5, Bernoulli Society for Mathematical Statistics
    and Probability, 2019, pp. 1659–96, doi:<a href="http://dx.doi.org/10.1016/j.spa.2018.05.012">http://dx.doi.org/10.1016/j.spa.2018.05.012</a>.
  short: A. Hening, M. Kolb, Stochastic Processes and Their Applications 129 (2019)
    1659–1696.
date_created: 2022-09-12T07:46:44Z
date_updated: 2022-09-12T07:46:47Z
department:
- _id: '96'
doi: http://dx.doi.org/10.1016/j.spa.2018.05.012
intvolume: '       129'
issue: '5'
language:
- iso: eng
page: 1659-1696
publication: Stochastic Processes and their Applications
publication_status: published
publisher: Bernoulli Society for Mathematical Statistics and Probability
status: public
title: Quasistationary distributions for one-dimensional diffusions with two singular
  boundary points
type: journal_article
user_id: '85821'
volume: 129
year: '2019'
...
---
_id: '33335'
abstract:
- lang: eng
  text: For a class of one-dimensional autoregressive sequences (Xn), we consider
    the tail behaviour of the stopping time T0=min{n≥1:Xn≤0}. We discuss existing
    general analytical approaches to this and related problems and propose a new one,
    which is based on a renewal-type decomposition for the moment generating function
    of T0 and on the analytical Fredholm alternative. Using this method, we show that
    Px(T0=n)∼V(x)Rn0 for some 0<R0<1 and a positive R0-harmonic function V. Further,
    we prove that our conditions on the tail behaviour of the innovations are sharp
    in the sense that fatter tails produce non-exponential decay factors.
author:
- first_name: Günter
  full_name: Hinrichs, Günter
  last_name: Hinrichs
- first_name: Martin
  full_name: Kolb, Martin
  id: '48880'
  last_name: Kolb
- first_name: Vitali
  full_name: Wachtel, Vitali
  last_name: Wachtel
citation:
  ama: Hinrichs G, Kolb M, Wachtel V. Persistence of one-dimensional AR(1)-processes.
    <i>Journal of Theoretical Probability</i>. 2018;33:65–102. doi:<a href="https://link.springer.com/article/10.1007/s10959-018-0850-0">https://link.springer.com/article/10.1007/s10959-018-0850-0</a>
  apa: Hinrichs, G., Kolb, M., &#38; Wachtel, V. (2018). Persistence of one-dimensional
    AR(1)-processes. <i>Journal of Theoretical Probability</i>, <i>33</i>, 65–102.
    <a href="https://link.springer.com/article/10.1007/s10959-018-0850-0">https://link.springer.com/article/10.1007/s10959-018-0850-0</a>
  bibtex: '@article{Hinrichs_Kolb_Wachtel_2018, title={Persistence of one-dimensional
    AR(1)-processes}, volume={33}, DOI={<a href="https://link.springer.com/article/10.1007/s10959-018-0850-0">https://link.springer.com/article/10.1007/s10959-018-0850-0</a>},
    journal={Journal of Theoretical Probability}, publisher={Springer Science + Business
    Media}, author={Hinrichs, Günter and Kolb, Martin and Wachtel, Vitali}, year={2018},
    pages={65–102} }'
  chicago: 'Hinrichs, Günter, Martin Kolb, and Vitali Wachtel. “Persistence of One-Dimensional
    AR(1)-Processes.” <i>Journal of Theoretical Probability</i> 33 (2018): 65–102.
    <a href="https://link.springer.com/article/10.1007/s10959-018-0850-0">https://link.springer.com/article/10.1007/s10959-018-0850-0</a>.'
  ieee: 'G. Hinrichs, M. Kolb, and V. Wachtel, “Persistence of one-dimensional AR(1)-processes,”
    <i>Journal of Theoretical Probability</i>, vol. 33, pp. 65–102, 2018, doi: <a
    href="https://link.springer.com/article/10.1007/s10959-018-0850-0">https://link.springer.com/article/10.1007/s10959-018-0850-0</a>.'
  mla: Hinrichs, Günter, et al. “Persistence of One-Dimensional AR(1)-Processes.”
    <i>Journal of Theoretical Probability</i>, vol. 33, Springer Science + Business
    Media, 2018, pp. 65–102, doi:<a href="https://link.springer.com/article/10.1007/s10959-018-0850-0">https://link.springer.com/article/10.1007/s10959-018-0850-0</a>.
  short: G. Hinrichs, M. Kolb, V. Wachtel, Journal of Theoretical Probability 33 (2018)
    65–102.
date_created: 2022-09-12T07:50:38Z
date_updated: 2022-09-12T07:52:44Z
department:
- _id: '96'
doi: https://link.springer.com/article/10.1007/s10959-018-0850-0
intvolume: '        33'
language:
- iso: eng
page: 65–102
publication: Journal of Theoretical Probability
publication_status: published
publisher: Springer Science + Business Media
status: public
title: Persistence of one-dimensional AR(1)-processes
type: journal_article
user_id: '85821'
volume: 33
year: '2018'
...
---
_id: '33336'
abstract:
- lang: eng
  text: The dipole approximation is employed to describe interactions between atoms
    and radiation. It essentially consists of neglecting the spatial variation of
    the external field over the atom. Heuristically, this is justified by arguing
    that the wavelength is considerably larger than the atomic length scale, which
    holds under usual experimental conditions. We prove the dipole approximation in
    the limit of infinite wavelengths compared to the atomic length scale and estimate
    the rate of convergence. Our results include N-body Coulomb potentials and experimentally
    relevant electromagnetic fields such as plane waves and laser pulses.
author:
- first_name: Lea
  full_name: Boßmann, Lea
  last_name: Boßmann
- first_name: Robert
  full_name: Grummt, Robert
  last_name: Grummt
- first_name: Martin
  full_name: Kolb, Martin
  id: '48880'
  last_name: Kolb
citation:
  ama: Boßmann L, Grummt R, Kolb M. On the dipole approximation with error estimates.
    <i>Letters in Mathematical Physics</i>. 2017;108:185–193. doi:<a href="https://link.springer.com/article/10.1007/s11005-017-0999-y">https://link.springer.com/article/10.1007/s11005-017-0999-y</a>
  apa: Boßmann, L., Grummt, R., &#38; Kolb, M. (2017). On the dipole approximation
    with error estimates. <i>Letters in Mathematical Physics</i>, <i>108</i>, 185–193.
    <a href="https://link.springer.com/article/10.1007/s11005-017-0999-y">https://link.springer.com/article/10.1007/s11005-017-0999-y</a>
  bibtex: '@article{Boßmann_Grummt_Kolb_2017, title={On the dipole approximation with
    error estimates}, volume={108}, DOI={<a href="https://link.springer.com/article/10.1007/s11005-017-0999-y">https://link.springer.com/article/10.1007/s11005-017-0999-y</a>},
    journal={Letters in Mathematical Physics}, author={Boßmann, Lea and Grummt, Robert
    and Kolb, Martin}, year={2017}, pages={185–193} }'
  chicago: 'Boßmann, Lea, Robert Grummt, and Martin Kolb. “On the Dipole Approximation
    with Error Estimates.” <i>Letters in Mathematical Physics</i> 108 (2017): 185–193.
    <a href="https://link.springer.com/article/10.1007/s11005-017-0999-y">https://link.springer.com/article/10.1007/s11005-017-0999-y</a>.'
  ieee: 'L. Boßmann, R. Grummt, and M. Kolb, “On the dipole approximation with error
    estimates,” <i>Letters in Mathematical Physics</i>, vol. 108, pp. 185–193, 2017,
    doi: <a href="https://link.springer.com/article/10.1007/s11005-017-0999-y">https://link.springer.com/article/10.1007/s11005-017-0999-y</a>.'
  mla: Boßmann, Lea, et al. “On the Dipole Approximation with Error Estimates.” <i>Letters
    in Mathematical Physics</i>, vol. 108, 2017, pp. 185–193, doi:<a href="https://link.springer.com/article/10.1007/s11005-017-0999-y">https://link.springer.com/article/10.1007/s11005-017-0999-y</a>.
  short: L. Boßmann, R. Grummt, M. Kolb, Letters in Mathematical Physics 108 (2017)
    185–193.
date_created: 2022-09-12T08:08:05Z
date_updated: 2022-09-12T08:08:09Z
department:
- _id: '96'
doi: https://link.springer.com/article/10.1007/s11005-017-0999-y
intvolume: '       108'
language:
- iso: eng
page: 185–193
publication: Letters in Mathematical Physics
publication_status: published
status: public
title: On the dipole approximation with error estimates
type: journal_article
user_id: '85821'
volume: 108
year: '2017'
...
---
_id: '33342'
abstract:
- lang: eng
  text: In this work we consider a one-dimensional Brownian motion with constant drift
    moving among a Poissonian cloud of obstacles. Our main result proves convergence
    of the law of processes conditional on survival up to time t as t converges to
    infinity in the critical case where the drift coincides with the intensity of
    the Poisson process. This complements a previous result of T. Povel, who considered
    the same question in the case where the drift is strictly smaller than the intensity.
    We also show that the end point of the process conditioned on survival up to time
    t rescaled by √t converges in distribution to a non-trivial random variable, as
    t tends to infinity, which is in fact invariant with respect to the drift h>0.
    We thus prove that it is sub-ballistic and estimate the speed of escape. The latter
    is in a sharp contrast with discrete models of dimension larger or equal to 2
    when the behaviour at criticality is ballistic, see [7], and even to many one
    dimensional models which exhibit ballistic behaviour at criticality, see [8].
author:
- first_name: Mladen
  full_name: Savov, Mladen
  last_name: Savov
- first_name: Martin
  full_name: Kolb, Martin
  id: '48880'
  last_name: Kolb
citation:
  ama: Savov M, Kolb M. Conditional survival distributions of Brownian trajectories
    in a one dimensional Poissonian environment in the critical case. <i>Electronic
    Journal of Probability</i>. 2017;22. doi:<a href="https://doi.org/10.1214/17-EJP4468">https://doi.org/10.1214/17-EJP4468</a>
  apa: Savov, M., &#38; Kolb, M. (2017). Conditional survival distributions of Brownian
    trajectories in a one dimensional Poissonian environment in the critical case.
    <i>Electronic Journal of Probability</i>, <i>22</i>. <a href="https://doi.org/10.1214/17-EJP4468">https://doi.org/10.1214/17-EJP4468</a>
  bibtex: '@article{Savov_Kolb_2017, title={Conditional survival distributions of
    Brownian trajectories in a one dimensional Poissonian environment in the critical
    case}, volume={22}, DOI={<a href="https://doi.org/10.1214/17-EJP4468">https://doi.org/10.1214/17-EJP4468</a>},
    journal={Electronic Journal of Probability}, publisher={ Institute of Mathematical
    Statistics &#38; Bernoulli Society}, author={Savov, Mladen and Kolb, Martin},
    year={2017} }'
  chicago: Savov, Mladen, and Martin Kolb. “Conditional Survival Distributions of
    Brownian Trajectories in a One Dimensional Poissonian Environment in the Critical
    Case.” <i>Electronic Journal of Probability</i> 22 (2017). <a href="https://doi.org/10.1214/17-EJP4468">https://doi.org/10.1214/17-EJP4468</a>.
  ieee: 'M. Savov and M. Kolb, “Conditional survival distributions of Brownian trajectories
    in a one dimensional Poissonian environment in the critical case,” <i>Electronic
    Journal of Probability</i>, vol. 22, 2017, doi: <a href="https://doi.org/10.1214/17-EJP4468">https://doi.org/10.1214/17-EJP4468</a>.'
  mla: Savov, Mladen, and Martin Kolb. “Conditional Survival Distributions of Brownian
    Trajectories in a One Dimensional Poissonian Environment in the Critical Case.”
    <i>Electronic Journal of Probability</i>, vol. 22,  Institute of Mathematical
    Statistics &#38; Bernoulli Society, 2017, doi:<a href="https://doi.org/10.1214/17-EJP4468">https://doi.org/10.1214/17-EJP4468</a>.
  short: M. Savov, M. Kolb, Electronic Journal of Probability 22 (2017).
date_created: 2022-09-13T07:47:39Z
date_updated: 2022-09-13T07:47:46Z
department:
- _id: '96'
doi: https://doi.org/10.1214/17-EJP4468
intvolume: '        22'
language:
- iso: eng
publication: Electronic Journal of Probability
publication_status: published
publisher: ' Institute of Mathematical Statistics & Bernoulli Society'
status: public
title: Conditional survival distributions of Brownian trajectories in a one dimensional
  Poissonian environment in the critical case
type: journal_article
user_id: '85821'
volume: 22
year: '2017'
...
---
_id: '33343'
abstract:
- lang: eng
  text: "Using an operator-theoretic framework in a Hilbert-space setting, we perform
    a\r\ndetailed spectral analysis of the one-dimensional Laplacian in a bounded
    interval, subject to\r\nspecific non-self-adjoint connected boundary conditions
    modelling a random jump from the\r\nboundary to a point inside the interval. In
    accordance with previous works, we find that all the\r\neigenvalues are real.
    As the new results, we derive and analyse the adjoint operator, determine\r\nthe
    geometric and algebraic multiplicities of the eigenvalues, write down formulae
    for the\r\neigenfunctions together with the generalised eigenfunctions and study
    their basis properties.\r\nIt turns out that the latter heavily depend on whether
    the distance of the interior point to the\r\ncentre of the interval divided by
    the length of the interval is rational or irrational. Finally,\r\nwe find a closed
    formula for the metric operator that provides a similarity transform of the\r\nproblem
    to a self-adjoint operator."
author:
- first_name: Martin
  full_name: Kolb, Martin
  id: '48880'
  last_name: Kolb
- first_name: David
  full_name: Krejčiřík, David
  last_name: Krejčiřík
citation:
  ama: Kolb M, Krejčiřík D. Spectral analysis of the diffusion operator with random
    jumps from the boundary. <i>Mathematische Zeitschrift</i>. 2016;284:877-900. doi:<a
    href="https://link.springer.com/content/pdf/10.1007/s00209-016-1677-y.pdf">https://link.springer.com/content/pdf/10.1007/s00209-016-1677-y.pdf</a>
  apa: Kolb, M., &#38; Krejčiřík, D. (2016). Spectral analysis of the diffusion operator
    with random jumps from the boundary. <i>Mathematische Zeitschrift</i>, <i>284</i>,
    877–900. <a href="https://link.springer.com/content/pdf/10.1007/s00209-016-1677-y.pdf">https://link.springer.com/content/pdf/10.1007/s00209-016-1677-y.pdf</a>
  bibtex: '@article{Kolb_Krejčiřík_2016, title={Spectral analysis of the diffusion
    operator with random jumps from the boundary}, volume={284}, DOI={<a href="https://link.springer.com/content/pdf/10.1007/s00209-016-1677-y.pdf">https://link.springer.com/content/pdf/10.1007/s00209-016-1677-y.pdf</a>},
    journal={Mathematische Zeitschrift}, publisher={Springer}, author={Kolb, Martin
    and Krejčiřík, David}, year={2016}, pages={877–900} }'
  chicago: 'Kolb, Martin, and David Krejčiřík. “Spectral Analysis of the Diffusion
    Operator with Random Jumps from the Boundary.” <i>Mathematische Zeitschrift</i>
    284 (2016): 877–900. <a href="https://link.springer.com/content/pdf/10.1007/s00209-016-1677-y.pdf">https://link.springer.com/content/pdf/10.1007/s00209-016-1677-y.pdf</a>.'
  ieee: 'M. Kolb and D. Krejčiřík, “Spectral analysis of the diffusion operator with
    random jumps from the boundary,” <i>Mathematische Zeitschrift</i>, vol. 284, pp.
    877–900, 2016, doi: <a href="https://link.springer.com/content/pdf/10.1007/s00209-016-1677-y.pdf">https://link.springer.com/content/pdf/10.1007/s00209-016-1677-y.pdf</a>.'
  mla: Kolb, Martin, and David Krejčiřík. “Spectral Analysis of the Diffusion Operator
    with Random Jumps from the Boundary.” <i>Mathematische Zeitschrift</i>, vol. 284,
    Springer, 2016, pp. 877–900, doi:<a href="https://link.springer.com/content/pdf/10.1007/s00209-016-1677-y.pdf">https://link.springer.com/content/pdf/10.1007/s00209-016-1677-y.pdf</a>.
  short: M. Kolb, D. Krejčiřík, Mathematische Zeitschrift 284 (2016) 877–900.
date_created: 2022-09-13T07:56:56Z
date_updated: 2022-09-13T07:56:59Z
department:
- _id: '96'
doi: https://link.springer.com/content/pdf/10.1007/s00209-016-1677-y.pdf
intvolume: '       284'
language:
- iso: eng
page: 877-900
publication: Mathematische Zeitschrift
publication_status: published
publisher: Springer
status: public
title: Spectral analysis of the diffusion operator with random jumps from the boundary
type: journal_article
user_id: '85821'
volume: 284
year: '2016'
...
---
_id: '33344'
abstract:
- lang: eng
  text: The hard disk model is a 2D Gibbsian process of particles interacting via
    pure hard core repulsion. At high particle density the model is believed to show
    orientational order, however, it is known not to exhibit positional order. Here
    we investigate to what extent particle positions may fluctuate. We consider a
    finite volume version of the model in a box of dimensions 2n ×  2n with arbitrary
    boundary configuration, and we show that the mean square displacement of particles
    near the center of the box is bounded from below by c log n. The result generalizes
    to a large class of models with fairly arbitrary interaction.
author:
- first_name: Thomas
  full_name: Richthammer, Thomas
  id: '62054'
  last_name: Richthammer
citation:
  ama: Richthammer T. Lower Bound on the Mean Square Displacement of Particles in
    the Hard Disk Model. <i>Communications in Mathematical Physics </i>. 2016;345:1077-1099.
    doi:<a href="https://link.springer.com/article/10.1007/s00220-016-2584-0">https://link.springer.com/article/10.1007/s00220-016-2584-0</a>
  apa: Richthammer, T. (2016). Lower Bound on the Mean Square Displacement of Particles
    in the Hard Disk Model. <i>Communications in Mathematical Physics </i>, <i>345</i>,
    1077–1099. <a href="https://link.springer.com/article/10.1007/s00220-016-2584-0">https://link.springer.com/article/10.1007/s00220-016-2584-0</a>
  bibtex: '@article{Richthammer_2016, title={Lower Bound on the Mean Square Displacement
    of Particles in the Hard Disk Model}, volume={345}, DOI={<a href="https://link.springer.com/article/10.1007/s00220-016-2584-0">https://link.springer.com/article/10.1007/s00220-016-2584-0</a>},
    journal={Communications in Mathematical Physics }, author={Richthammer, Thomas},
    year={2016}, pages={1077–1099} }'
  chicago: 'Richthammer, Thomas. “Lower Bound on the Mean Square Displacement of Particles
    in the Hard Disk Model.” <i>Communications in Mathematical Physics </i> 345 (2016):
    1077–99. <a href="https://link.springer.com/article/10.1007/s00220-016-2584-0">https://link.springer.com/article/10.1007/s00220-016-2584-0</a>.'
  ieee: 'T. Richthammer, “Lower Bound on the Mean Square Displacement of Particles
    in the Hard Disk Model,” <i>Communications in Mathematical Physics </i>, vol.
    345, pp. 1077–1099, 2016, doi: <a href="https://link.springer.com/article/10.1007/s00220-016-2584-0">https://link.springer.com/article/10.1007/s00220-016-2584-0</a>.'
  mla: Richthammer, Thomas. “Lower Bound on the Mean Square Displacement of Particles
    in the Hard Disk Model.” <i>Communications in Mathematical Physics </i>, vol.
    345, 2016, pp. 1077–99, doi:<a href="https://link.springer.com/article/10.1007/s00220-016-2584-0">https://link.springer.com/article/10.1007/s00220-016-2584-0</a>.
  short: T. Richthammer, Communications in Mathematical Physics  345 (2016) 1077–1099.
date_created: 2022-09-13T08:01:29Z
date_updated: 2022-09-13T08:01:36Z
department:
- _id: '96'
doi: https://link.springer.com/article/10.1007/s00220-016-2584-0
intvolume: '       345'
language:
- iso: eng
page: 1077-1099
publication: 'Communications in Mathematical Physics '
publication_status: published
status: public
title: Lower Bound on the Mean Square Displacement of Particles in the Hard Disk Model
type: journal_article
user_id: '85821'
volume: 345
year: '2016'
...
---
_id: '33357'
abstract:
- lang: eng
  text: 'In this note we investigate the behaviour of Brownian motion conditioned
    on a growth constraint of its local time which has been previously investigated
    by Berestycki and Benjamini. For a class of non-decreasing positive functions
    f(t);t>0, we consider the Wiener measure under the condition that the Brownian
    local time is dominated by the function f up to time T. In the case where f(t)/t3/2
    is integrable we describe the limiting process as T goes to infinity. Moreover,
    we prove two conjectures in [BB10] in the case for a class of functions f, for
    which f(t)/t3/2 just fails to be integrable. Our methodology is more general as
    it relies on the study of the asymptotic of the probability of subordinators to
    stay above a given curve. Immediately or with adaptations one can study questions
    like the Brownian motioned conditioned on a growth constraint of its local time
    at the maximum or more generally a Levy process conditioned on a growth constraint
    of its local time at the maximum or at zero. We discuss briefly the former. '
author:
- first_name: Martin
  full_name: Kolb, Martin
  id: '48880'
  last_name: Kolb
- first_name: Mladen
  full_name: Savov, Mladen
  last_name: Savov
citation:
  ama: Kolb M, Savov M. Transience and recurrence of a Brownian path with limited
    local time. <i>The Annals of Probability</i>. 2016;44(6). doi:<a href="http://dx.doi.org/10.1214/15-AOP1069">http://dx.doi.org/10.1214/15-AOP1069</a>
  apa: Kolb, M., &#38; Savov, M. (2016). Transience and recurrence of a Brownian path
    with limited local time. <i>The Annals of Probability</i>, <i>44</i>(6). <a href="http://dx.doi.org/10.1214/15-AOP1069">http://dx.doi.org/10.1214/15-AOP1069</a>
  bibtex: '@article{Kolb_Savov_2016, title={Transience and recurrence of a Brownian
    path with limited local time}, volume={44}, DOI={<a href="http://dx.doi.org/10.1214/15-AOP1069">http://dx.doi.org/10.1214/15-AOP1069</a>},
    number={6}, journal={The Annals of Probability}, publisher={Institute of Mathematical
    Statistics}, author={Kolb, Martin and Savov, Mladen}, year={2016} }'
  chicago: Kolb, Martin, and Mladen Savov. “Transience and Recurrence of a Brownian
    Path with Limited Local Time.” <i>The Annals of Probability</i> 44, no. 6 (2016).
    <a href="http://dx.doi.org/10.1214/15-AOP1069">http://dx.doi.org/10.1214/15-AOP1069</a>.
  ieee: 'M. Kolb and M. Savov, “Transience and recurrence of a Brownian path with
    limited local time,” <i>The Annals of Probability</i>, vol. 44, no. 6, 2016, doi:
    <a href="http://dx.doi.org/10.1214/15-AOP1069">http://dx.doi.org/10.1214/15-AOP1069</a>.'
  mla: Kolb, Martin, and Mladen Savov. “Transience and Recurrence of a Brownian Path
    with Limited Local Time.” <i>The Annals of Probability</i>, vol. 44, no. 6, Institute
    of Mathematical Statistics, 2016, doi:<a href="http://dx.doi.org/10.1214/15-AOP1069">http://dx.doi.org/10.1214/15-AOP1069</a>.
  short: M. Kolb, M. Savov, The Annals of Probability 44 (2016).
date_created: 2022-09-14T04:22:23Z
date_updated: 2022-09-14T04:22:26Z
department:
- _id: '96'
doi: http://dx.doi.org/10.1214/15-AOP1069
intvolume: '        44'
issue: '6'
language:
- iso: eng
publication: The Annals of Probability
publication_status: published
publisher: Institute of Mathematical Statistics
status: public
title: Transience and recurrence of a Brownian path with limited local time
type: journal_article
user_id: '85821'
volume: 44
year: '2016'
...
---
_id: '33359'
abstract:
- lang: eng
  text: 'We consider Gibbs distributions on permutations of a locally finite infinite
    set X⊂R, where a permutation σ of X is assigned (formal) energy ∑x∈XV(σ(x)−x).
    This is motivated by Feynman’s path representation of the quantum Bose gas; the
    choice X:=Z and V(x):=αx2 is of principal interest. Under suitable regularity
    conditions on the set X and the potential V, we establish existence and a full
    classification of the infinite-volume Gibbs measures for this problem, including
    a result on the number of infinite cycles of typical permutations. Unlike earlier
    results, our conclusions are not limited to small densities and/or high temperatures. '
author:
- first_name: Thomas
  full_name: Richthammer, Thomas
  id: '62054'
  last_name: Richthammer
- first_name: Marek
  full_name: Biskup, Marek
  last_name: Biskup
citation:
  ama: Richthammer T, Biskup M. Gibbs measures on permutations over one-dimensional
    discrete point sets. <i>Communications in Mathematical Physics</i>. 2015;25(2):898-929.
    doi:<a href="https://doi.org/10.48550/arXiv.1310.0248">https://doi.org/10.48550/arXiv.1310.0248</a>
  apa: Richthammer, T., &#38; Biskup, M. (2015). Gibbs measures on permutations over
    one-dimensional discrete point sets. <i>Communications in Mathematical Physics</i>,
    <i>25</i>(2), 898–929. <a href="https://doi.org/10.48550/arXiv.1310.0248">https://doi.org/10.48550/arXiv.1310.0248</a>
  bibtex: '@article{Richthammer_Biskup_2015, title={Gibbs measures on permutations
    over one-dimensional discrete point sets}, volume={25}, DOI={<a href="https://doi.org/10.48550/arXiv.1310.0248">https://doi.org/10.48550/arXiv.1310.0248</a>},
    number={2}, journal={Communications in Mathematical Physics}, publisher={Springer
    Science+Business Media}, author={Richthammer, Thomas and Biskup, Marek}, year={2015},
    pages={898–929} }'
  chicago: 'Richthammer, Thomas, and Marek Biskup. “Gibbs Measures on Permutations
    over One-Dimensional Discrete Point Sets.” <i>Communications in Mathematical Physics</i>
    25, no. 2 (2015): 898–929. <a href="https://doi.org/10.48550/arXiv.1310.0248">https://doi.org/10.48550/arXiv.1310.0248</a>.'
  ieee: 'T. Richthammer and M. Biskup, “Gibbs measures on permutations over one-dimensional
    discrete point sets,” <i>Communications in Mathematical Physics</i>, vol. 25,
    no. 2, pp. 898–929, 2015, doi: <a href="https://doi.org/10.48550/arXiv.1310.0248">https://doi.org/10.48550/arXiv.1310.0248</a>.'
  mla: Richthammer, Thomas, and Marek Biskup. “Gibbs Measures on Permutations over
    One-Dimensional Discrete Point Sets.” <i>Communications in Mathematical Physics</i>,
    vol. 25, no. 2, Springer Science+Business Media, 2015, pp. 898–929, doi:<a href="https://doi.org/10.48550/arXiv.1310.0248">https://doi.org/10.48550/arXiv.1310.0248</a>.
  short: T. Richthammer, M. Biskup, Communications in Mathematical Physics 25 (2015)
    898–929.
date_created: 2022-09-14T04:57:58Z
date_updated: 2022-09-14T04:58:02Z
department:
- _id: '96'
doi: https://doi.org/10.48550/arXiv.1310.0248
intvolume: '        25'
issue: '2'
language:
- iso: eng
page: 898-929
publication: Communications in Mathematical Physics
publication_status: published
publisher: Springer Science+Business Media
status: public
title: Gibbs measures on permutations over one-dimensional discrete point sets
type: journal_article
user_id: '85821'
volume: 25
year: '2015'
...
---
_id: '33358'
abstract:
- lang: eng
  text: 'We study the workload processes of two M/G/1 queueing systems with restricted
    capacity: in Model 1 any service requirement that would exceed a certain capacity
    threshold is truncated; in Model 2 new arrivals do not enter the system if they
    have to wait more than a fixed threshold time in line. For Model 1 we obtain several
    results concerning the rate of convergence to equilibrium. In particular, we derive
    uniform bounds for geometric ergodicity with respect to certain subclasses. For
    Model 2 geometric ergodicity follows from the finiteness of the moment-generating
    function of the service time distribution. We derive bounds for the convergence
    rates in special cases. The proofs use the coupling method.'
author:
- first_name: Martin
  full_name: Kolb, Martin
  id: '48880'
  last_name: Kolb
- first_name: Wolfgang
  full_name: Stadje, Wolfgang
  last_name: Stadje
- first_name: Achim
  full_name: Wübker, Achim
  last_name: Wübker
citation:
  ama: Kolb M, Stadje W, Wübker A. The rate of convergence to stationarity for M/G/1
    models with admission controls via coupling. <i>Stochastic Models</i>. 2015;32(1):121-135.
    doi:<a href="http://dx.doi.org/10.1080/15326349.2015.1090322">http://dx.doi.org/10.1080/15326349.2015.1090322</a>
  apa: Kolb, M., Stadje, W., &#38; Wübker, A. (2015). The rate of convergence to stationarity
    for M/G/1 models with admission controls via coupling. <i>Stochastic Models</i>,
    <i>32</i>(1), 121–135. <a href="http://dx.doi.org/10.1080/15326349.2015.1090322">http://dx.doi.org/10.1080/15326349.2015.1090322</a>
  bibtex: '@article{Kolb_Stadje_Wübker_2015, title={The rate of convergence to stationarity
    for M/G/1 models with admission controls via coupling}, volume={32}, DOI={<a href="http://dx.doi.org/10.1080/15326349.2015.1090322">http://dx.doi.org/10.1080/15326349.2015.1090322</a>},
    number={1}, journal={Stochastic Models}, publisher={INFORMS}, author={Kolb, Martin
    and Stadje, Wolfgang and Wübker, Achim}, year={2015}, pages={121–135} }'
  chicago: 'Kolb, Martin, Wolfgang Stadje, and Achim Wübker. “The Rate of Convergence
    to Stationarity for M/G/1 Models with Admission Controls via Coupling.” <i>Stochastic
    Models</i> 32, no. 1 (2015): 121–35. <a href="http://dx.doi.org/10.1080/15326349.2015.1090322">http://dx.doi.org/10.1080/15326349.2015.1090322</a>.'
  ieee: 'M. Kolb, W. Stadje, and A. Wübker, “The rate of convergence to stationarity
    for M/G/1 models with admission controls via coupling,” <i>Stochastic Models</i>,
    vol. 32, no. 1, pp. 121–135, 2015, doi: <a href="http://dx.doi.org/10.1080/15326349.2015.1090322">http://dx.doi.org/10.1080/15326349.2015.1090322</a>.'
  mla: Kolb, Martin, et al. “The Rate of Convergence to Stationarity for M/G/1 Models
    with Admission Controls via Coupling.” <i>Stochastic Models</i>, vol. 32, no.
    1, INFORMS, 2015, pp. 121–35, doi:<a href="http://dx.doi.org/10.1080/15326349.2015.1090322">http://dx.doi.org/10.1080/15326349.2015.1090322</a>.
  short: M. Kolb, W. Stadje, A. Wübker, Stochastic Models 32 (2015) 121–135.
date_created: 2022-09-14T04:52:15Z
date_updated: 2022-09-14T04:52:19Z
department:
- _id: '96'
doi: http://dx.doi.org/10.1080/15326349.2015.1090322
intvolume: '        32'
issue: '1'
language:
- iso: eng
page: 121-135
publication: Stochastic Models
publication_status: published
publisher: INFORMS
status: public
title: The rate of convergence to stationarity for M/G/1 models with admission controls
  via coupling
type: journal_article
user_id: '85821'
volume: 32
year: '2015'
...
---
_id: '33360'
abstract:
- lang: eng
  text: We prove a local limit theorem for the area of the positive excursion of random
    walks with zero mean and finite variance. Our main result complements previous
    work of Caravenna and Chaumont; Sohier, as well as Kim and Pittel.
author:
- first_name: Martin
  full_name: Kolb, Martin
  id: '48880'
  last_name: Kolb
- first_name: Denis
  full_name: Denisov, Denis
  last_name: Denisov
- first_name: Vitali
  full_name: Wachtel, Vitali
  last_name: Wachtel
citation:
  ama: Kolb M, Denisov D, Wachtel V. Local asymptotics for the area of random walk
    excursions. <i>Journal of the London Mathematical Society</i>. 2015;91(2):495-513.
  apa: Kolb, M., Denisov, D., &#38; Wachtel, V. (2015). Local asymptotics for the
    area of random walk excursions. <i>Journal of the London Mathematical Society</i>,
    <i>91</i>(2), 495–513.
  bibtex: '@article{Kolb_Denisov_Wachtel_2015, title={Local asymptotics for the area
    of random walk excursions}, volume={91}, number={2}, journal={Journal of the London
    Mathematical Society}, publisher={London Mathematical Society}, author={Kolb,
    Martin and Denisov, Denis and Wachtel, Vitali}, year={2015}, pages={495–513} }'
  chicago: 'Kolb, Martin, Denis Denisov, and Vitali Wachtel. “Local Asymptotics for
    the Area of Random Walk Excursions.” <i>Journal of the London Mathematical Society</i>
    91, no. 2 (2015): 495–513.'
  ieee: M. Kolb, D. Denisov, and V. Wachtel, “Local asymptotics for the area of random
    walk excursions,” <i>Journal of the London Mathematical Society</i>, vol. 91,
    no. 2, pp. 495–513, 2015.
  mla: Kolb, Martin, et al. “Local Asymptotics for the Area of Random Walk Excursions.”
    <i>Journal of the London Mathematical Society</i>, vol. 91, no. 2, London Mathematical
    Society, 2015, pp. 495–513.
  short: M. Kolb, D. Denisov, V. Wachtel, Journal of the London Mathematical Society
    91 (2015) 495–513.
date_created: 2022-09-14T05:01:41Z
date_updated: 2022-09-14T05:01:45Z
department:
- _id: '96'
intvolume: '        91'
issue: '2'
language:
- iso: eng
page: 495-513
publication: Journal of the London Mathematical Society
publication_status: published
publisher: London Mathematical Society
status: public
title: Local asymptotics for the area of random walk excursions
type: journal_article
user_id: '85821'
volume: 91
year: '2015'
...
---
_id: '33361'
abstract:
- lang: eng
  text: Following Bertoin who considered the ergodicity and exponential decay of Lévy
    processes in a finite domain, we consider general Lévy processes and their ergodicity
    and exponential decay in a finite interval. More precisely, given Ta=inf{t>0:Xt∉.
    Under general conditions, e.g. absolute continuity of the transition semigroup
    of the unkilled Lévy process, we prove that the killed semigroup is a compact
    operator. Thus, we prove stronger results in view of the exponential ergodicity
    and estimates of the speed of convergence. Our results are presented in a Lévy
    processes setting but are well applicable for Markov processes in a finite interval
    under information about Lebesgue irreducibility of the killed semigroup and that
    the killed process is a double Feller process. For example, this scheme is applicable
    to a work of Pistorius.<br />
author:
- first_name: Martin
  full_name: Kolb, Martin
  id: '48880'
  last_name: Kolb
- first_name: Mladen
  full_name: Savov, Mladen
  last_name: Savov
citation:
  ama: Kolb M, Savov M. Exponential ergodicity of killed Lévy processes in a finite
    interval. <i>Electronic Communications in Probability</i>. 2014;19(31):1-9. doi:<a
    href="http://dx.doi.org/10.1214/ECP.v19-3006">http://dx.doi.org/10.1214/ECP.v19-3006</a>
  apa: Kolb, M., &#38; Savov, M. (2014). Exponential ergodicity of killed Lévy processes
    in a finite interval. <i>Electronic Communications in Probability</i>, <i>19</i>(31),
    1–9. <a href="http://dx.doi.org/10.1214/ECP.v19-3006">http://dx.doi.org/10.1214/ECP.v19-3006</a>
  bibtex: '@article{Kolb_Savov_2014, title={Exponential ergodicity of killed Lévy
    processes in a finite interval}, volume={19}, DOI={<a href="http://dx.doi.org/10.1214/ECP.v19-3006">http://dx.doi.org/10.1214/ECP.v19-3006</a>},
    number={31}, journal={Electronic Communications in Probability}, publisher={Institute
    of Mathematical Statistics (IMS)}, author={Kolb, Martin and Savov, Mladen}, year={2014},
    pages={1–9} }'
  chicago: 'Kolb, Martin, and Mladen Savov. “Exponential Ergodicity of Killed Lévy
    Processes in a Finite Interval.” <i>Electronic Communications in Probability</i>
    19, no. 31 (2014): 1–9. <a href="http://dx.doi.org/10.1214/ECP.v19-3006">http://dx.doi.org/10.1214/ECP.v19-3006</a>.'
  ieee: 'M. Kolb and M. Savov, “Exponential ergodicity of killed Lévy processes in
    a finite interval,” <i>Electronic Communications in Probability</i>, vol. 19,
    no. 31, pp. 1–9, 2014, doi: <a href="http://dx.doi.org/10.1214/ECP.v19-3006">http://dx.doi.org/10.1214/ECP.v19-3006</a>.'
  mla: Kolb, Martin, and Mladen Savov. “Exponential Ergodicity of Killed Lévy Processes
    in a Finite Interval.” <i>Electronic Communications in Probability</i>, vol. 19,
    no. 31, Institute of Mathematical Statistics (IMS), 2014, pp. 1–9, doi:<a href="http://dx.doi.org/10.1214/ECP.v19-3006">http://dx.doi.org/10.1214/ECP.v19-3006</a>.
  short: M. Kolb, M. Savov, Electronic Communications in Probability 19 (2014) 1–9.
date_created: 2022-09-14T05:15:00Z
date_updated: 2022-09-14T05:15:06Z
department:
- _id: '96'
doi: http://dx.doi.org/10.1214/ECP.v19-3006
intvolume: '        19'
issue: '31'
language:
- iso: eng
page: 1-9
publication: Electronic Communications in Probability
publication_status: published
publisher: Institute of Mathematical Statistics (IMS)
status: public
title: Exponential ergodicity of killed Lévy processes in a finite interval
type: journal_article
user_id: '85821'
volume: 19
year: '2014'
...