[{"department":[{"_id":"96"}],"publication":"Theory of Probability and its Applications","publisher":"Society for Industrial and Applied Mathematics","author":[{"last_name":"Kolb","id":"48880","first_name":"Martin","full_name":"Kolb, Martin"},{"last_name":"Klump","id":"45067","first_name":"Alexander","full_name":"Klump, Alexander"}],"date_created":"2023-01-10T08:13:17Z","status":"public","publication_status":"published","volume":67,"user_id":"85821","title":"Uniqueness of the Inverse First Passage Time Problem and the Shape of the Shiryaev boundary","language":[{"iso":"eng"}],"page":"717-744","year":"2022","type":"journal_article","citation":{"mla":"Kolb, Martin, and Alexander Klump. “Uniqueness of the Inverse First Passage Time Problem and the Shape of the Shiryaev Boundary.” Theory of Probability and Its Applications, vol. 67, no. 4, Society for Industrial and Applied Mathematics, 2022, pp. 717–44.","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} }","ieee":"M. Kolb and A. Klump, “Uniqueness of the Inverse First Passage Time Problem and the Shape of the Shiryaev boundary,” Theory of Probability and its Applications, vol. 67, no. 4, pp. 717–744, 2022.","chicago":"Kolb, Martin, and Alexander Klump. “Uniqueness of the Inverse First Passage Time Problem and the Shape of the Shiryaev Boundary.” Theory of Probability and Its Applications 67, no. 4 (2022): 717–44.","ama":"Kolb M, Klump A. Uniqueness of the Inverse First Passage Time Problem and the Shape of the Shiryaev boundary. Theory of Probability and its Applications. 2022;67(4):717-744.","short":"M. Kolb, A. Klump, Theory of Probability and Its Applications 67 (2022) 717–744.","apa":"Kolb, M., & Klump, A. (2022). Uniqueness of the Inverse First Passage Time Problem and the Shape of the Shiryaev boundary. Theory of Probability and Its Applications, 67(4), 717–744."},"date_updated":"2023-01-10T08:13:30Z","_id":"35644","intvolume":" 67","issue":"4"},{"department":[{"_id":"96"}],"publication":"Electronic Journal of Probability","author":[{"last_name":"Kolb","id":"48880","first_name":"Martin","full_name":"Kolb, Martin"},{"last_name":"Liesenfeld","full_name":"Liesenfeld, Matthias","first_name":"Matthias"}],"publisher":"Institute of Mathematical Statistics","date_created":"2023-01-10T08:19:25Z","status":"public","publication_status":"published","abstract":[{"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.","lang":"eng"}],"user_id":"85821","title":"On non-extinction in a Fleming-Viot-type particle model with Bessel drift","language":[{"iso":"eng"}],"page":"1-28","citation":{"ieee":"M. Kolb and M. Liesenfeld, “On non-extinction in a Fleming-Viot-type particle model with Bessel drift,” Electronic Journal of Probability, no. 27, pp. 1–28, 2022, doi: https://doi.org/10.1214/22-EJP866.","short":"M. Kolb, M. Liesenfeld, Electronic Journal of Probability (2022) 1–28.","mla":"Kolb, Martin, and Matthias Liesenfeld. “On Non-Extinction in a Fleming-Viot-Type Particle Model with Bessel Drift.” Electronic Journal of Probability, no. 27, Institute of Mathematical Statistics, 2022, pp. 1–28, doi:https://doi.org/10.1214/22-EJP866.","bibtex":"@article{Kolb_Liesenfeld_2022, title={On non-extinction in a Fleming-Viot-type particle model with Bessel drift}, DOI={https://doi.org/10.1214/22-EJP866}, 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.” Electronic Journal of Probability, no. 27 (2022): 1–28. https://doi.org/10.1214/22-EJP866.","ama":"Kolb M, Liesenfeld M. On non-extinction in a Fleming-Viot-type particle model with Bessel drift. Electronic Journal of Probability. 2022;(27):1-28. doi:https://doi.org/10.1214/22-EJP866","apa":"Kolb, M., & Liesenfeld, M. (2022). On non-extinction in a Fleming-Viot-type particle model with Bessel drift. Electronic Journal of Probability, 27, 1–28. https://doi.org/10.1214/22-EJP866"},"type":"journal_article","year":"2022","_id":"35649","date_updated":"2023-01-10T08:19:38Z","issue":"27","doi":"https://doi.org/10.1214/22-EJP866"},{"author":[{"last_name":"Denisov","full_name":"Denisov, Denis","first_name":"Denis"},{"first_name":"Günter","full_name":"Hinrichs, Günter","last_name":"Hinrichs"},{"first_name":"Martin","full_name":"Kolb, Martin","last_name":"Kolb","id":"48880"},{"last_name":"Wachtel","first_name":"Vitali","full_name":"Wachtel, Vitali"}],"publisher":"Institute of Mathematical Statistics","publication":"Electronic Journal of Probability","department":[{"_id":"96"}],"volume":27,"publication_status":"published","status":"public","date_created":"2023-01-10T08:28:12Z","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."}],"title":"Persistence of autoregressive sequences with logarithmic tails","user_id":"85821","year":"2022","type":"journal_article","citation":{"short":"D. Denisov, G. Hinrichs, M. Kolb, V. Wachtel, Electronic Journal of Probability 27 (2022) 1–43.","ieee":"D. Denisov, G. Hinrichs, M. Kolb, and V. Wachtel, “Persistence of autoregressive sequences with logarithmic tails,” Electronic Journal of Probability, vol. 27, pp. 1–43, 2022, doi: https://doi.org/10.48550/arXiv.2203.14772.","ama":"Denisov D, Hinrichs G, Kolb M, Wachtel V. Persistence of autoregressive sequences with logarithmic tails. Electronic Journal of Probability. 2022;27:1-43. doi:https://doi.org/10.48550/arXiv.2203.14772","apa":"Denisov, D., Hinrichs, G., Kolb, M., & Wachtel, V. (2022). Persistence of autoregressive sequences with logarithmic tails. Electronic Journal of Probability, 27, 1–43. https://doi.org/10.48550/arXiv.2203.14772","chicago":"Denisov, Denis, Günter Hinrichs, Martin Kolb, and Vitali Wachtel. “Persistence of Autoregressive Sequences with Logarithmic Tails.” Electronic Journal of Probability 27 (2022): 1–43. https://doi.org/10.48550/arXiv.2203.14772.","mla":"Denisov, Denis, et al. “Persistence of Autoregressive Sequences with Logarithmic Tails.” Electronic Journal of Probability, vol. 27, Institute of Mathematical Statistics, 2022, pp. 1–43, doi:https://doi.org/10.48550/arXiv.2203.14772.","bibtex":"@article{Denisov_Hinrichs_Kolb_Wachtel_2022, title={Persistence of autoregressive sequences with logarithmic tails}, volume={27}, DOI={https://doi.org/10.48550/arXiv.2203.14772}, 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} }"},"page":"1-43","language":[{"iso":"eng"}],"_id":"35650","intvolume":" 27","date_updated":"2023-01-10T08:29:02Z","doi":"https://doi.org/10.48550/arXiv.2203.14772"},{"date_updated":"2022-09-08T06:06:13Z","oa":"1","language":[{"iso":"eng"}],"title":"Spectral Asymptotics for Kinetic Brownian Motion on Surfaces of Constant Curvature","related_material":{"link":[{"relation":"contains","url":"https://link.springer.com/article/10.1007/s00023-021-01121-5"}]},"department":[{"_id":"96"}],"publication_status":"published","intvolume":" 23","_id":"33278","issue":"4","main_file_link":[{"url":"https://link.springer.com/article/10.1007/s00023-021-01121-5","open_access":"1"}],"page":"1283-1296","year":"2021","type":"journal_article","citation":{"ama":"Kolb M, Weich T, Wolf L. Spectral Asymptotics for Kinetic Brownian Motion on Surfaces of Constant Curvature. Annales Henri Poincaré . 2021;23(4):1283-1296.","apa":"Kolb, M., Weich, T., & Wolf, L. (2021). Spectral Asymptotics for Kinetic Brownian Motion on Surfaces of Constant Curvature. Annales Henri Poincaré , 23(4), 1283–1296.","chicago":"Kolb, Martin, Tobias Weich, and Lasse Wolf. “Spectral Asymptotics for Kinetic Brownian Motion on Surfaces of Constant Curvature.” Annales Henri Poincaré 23, no. 4 (2021): 1283–96.","mla":"Kolb, Martin, et al. “Spectral Asymptotics for Kinetic Brownian Motion on Surfaces of Constant Curvature.” Annales Henri Poincaré , vol. 23, no. 4, Springer Science + Business Media, 2021, pp. 1283–96.","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} }","short":"M. Kolb, T. Weich, L. Wolf, Annales Henri Poincaré 23 (2021) 1283–1296.","ieee":"M. Kolb, T. Weich, and L. Wolf, “Spectral Asymptotics for Kinetic Brownian Motion on Surfaces of Constant Curvature,” Annales Henri Poincaré , vol. 23, no. 4, pp. 1283–1296, 2021."},"abstract":[{"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.","lang":"eng"}],"user_id":"85821","publication":"Annales Henri Poincaré ","author":[{"full_name":"Kolb, Martin","first_name":"Martin","id":"48880","last_name":"Kolb"},{"last_name":"Weich","first_name":"Tobias","full_name":"Weich, Tobias"},{"last_name":"Wolf","full_name":"Wolf, Lasse","first_name":"Lasse"}],"publisher":"Springer Science + Business Media","volume":23,"date_created":"2022-09-07T07:05:33Z","status":"public"},{"status":"public","date_created":"2022-09-26T06:53:59Z","volume":132,"publication_status":"published","author":[{"id":"62054","last_name":"Richthammer","full_name":"Richthammer, Thomas","first_name":"Thomas"},{"last_name":"Fiedler","first_name":"Michael","full_name":"Fiedler, Michael"}],"publisher":"Elsevier","department":[{"_id":"96"}],"publication":"Stochastic Processes and their Applications","user_id":"85821","title":"A lower bound on the displacement of particles in 2D Gibbsian particle systems","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."}],"language":[{"iso":"eng"}],"type":"journal_article","year":"2021","citation":{"mla":"Richthammer, Thomas, and Michael Fiedler. “A Lower Bound on the Displacement of Particles in 2D Gibbsian Particle Systems.” Stochastic Processes and Their Applications, vol. 132, Elsevier, 2021, pp. 1–32, doi:https://doi.org/10.1016/j.spa.2020.10.003.","bibtex":"@article{Richthammer_Fiedler_2021, title={A lower bound on the displacement of particles in 2D Gibbsian particle systems}, volume={132}, DOI={https://doi.org/10.1016/j.spa.2020.10.003}, 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.” Stochastic Processes and Their Applications 132 (2021): 1–32. https://doi.org/10.1016/j.spa.2020.10.003.","ama":"Richthammer T, Fiedler M. A lower bound on the displacement of particles in 2D Gibbsian particle systems. Stochastic Processes and their Applications. 2021;132:1-32. doi:https://doi.org/10.1016/j.spa.2020.10.003","apa":"Richthammer, T., & Fiedler, M. (2021). A lower bound on the displacement of particles in 2D Gibbsian particle systems. Stochastic Processes and Their Applications, 132, 1–32. https://doi.org/10.1016/j.spa.2020.10.003","ieee":"T. Richthammer and M. Fiedler, “A lower bound on the displacement of particles in 2D Gibbsian particle systems,” Stochastic Processes and their Applications, vol. 132, pp. 1–32, 2021, doi: https://doi.org/10.1016/j.spa.2020.10.003.","short":"T. Richthammer, M. Fiedler, Stochastic Processes and Their Applications 132 (2021) 1–32."},"page":"1-32","doi":"https://doi.org/10.1016/j.spa.2020.10.003","intvolume":" 132","_id":"33481","date_updated":"2022-09-26T06:54:06Z"},{"issue":"2","_id":"33282","intvolume":" 26","page":"1453-1472","citation":{"chicago":"Kolb, Martin, and Mladen Savov. “A Characterization of the Finiteness of Perpetual Integrals of Levy Processes.” Bernoulli 26, no. 2 (2020): 1453–72. https://doi.org/10.48550/arXiv.1903.03792.","ama":"Kolb M, Savov M. A Characterization of the Finiteness of Perpetual Integrals of Levy Processes. Bernoulli. 2020;26(2):1453-1472. doi:https://doi.org/10.48550/arXiv.1903.03792","apa":"Kolb, M., & Savov, M. (2020). A Characterization of the Finiteness of Perpetual Integrals of Levy Processes. Bernoulli, 26(2), 1453–1472. https://doi.org/10.48550/arXiv.1903.03792","mla":"Kolb, Martin, and Mladen Savov. “A Characterization of the Finiteness of Perpetual Integrals of Levy Processes.” Bernoulli, vol. 26, no. 2, Bernoulli Society for Mathematical Statistics and Probability, 2020, pp. 1453–72, doi:https://doi.org/10.48550/arXiv.1903.03792.","bibtex":"@article{Kolb_Savov_2020, title={A Characterization of the Finiteness of Perpetual Integrals of Levy Processes}, volume={26}, DOI={https://doi.org/10.48550/arXiv.1903.03792}, number={2}, journal={Bernoulli}, publisher={Bernoulli Society for Mathematical Statistics and Probability}, author={Kolb, Martin and Savov, Mladen}, year={2020}, pages={1453–1472} }","short":"M. Kolb, M. Savov, Bernoulli 26 (2020) 1453–1472.","ieee":"M. Kolb and M. Savov, “A Characterization of the Finiteness of Perpetual Integrals of Levy Processes,” Bernoulli, vol. 26, no. 2, pp. 1453–1472, 2020, doi: https://doi.org/10.48550/arXiv.1903.03792."},"type":"journal_article","year":"2020","user_id":"85821","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)."}],"date_created":"2022-09-08T06:36:37Z","status":"public","volume":26,"keyword":["L ́evy processes","Perpetual integrals","Potential measures"],"publication":"Bernoulli","author":[{"id":"48880","last_name":"Kolb","full_name":"Kolb, Martin","first_name":"Martin"},{"first_name":"Mladen","full_name":"Savov, Mladen","last_name":"Savov"}],"publisher":"Bernoulli Society for Mathematical Statistics and Probability","doi":"https://doi.org/10.48550/arXiv.1903.03792","date_updated":"2022-09-08T06:48:40Z","language":[{"iso":"eng"}],"title":"A Characterization of the Finiteness of Perpetual Integrals of Levy Processes","publication_status":"published","department":[{"_id":"96"}]},{"date_updated":"2022-09-12T07:13:30Z","doi":"https://doi.org/10.1016/j.ijar.2020.01.007","language":[{"iso":"eng"}],"title":"Generalized transitivity: A systematic comparison of concepts with an application to preferences in the Babington Smith model","department":[{"_id":"96"}],"publication_status":"published","intvolume":" 119","_id":"33330","issue":"2","page":"373-407","year":"2020","citation":{"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,” International Journal of Approximate Reasoning, vol. 119, no. 2, pp. 373–407, 2020, doi: https://doi.org/10.1016/j.ijar.2020.01.007.","short":"B. Haddenhorst, E. Hüllermeier, M. Kolb, International Journal of Approximate Reasoning 119 (2020) 373–407.","mla":"Haddenhorst, Björn, et al. “Generalized Transitivity: A Systematic Comparison of Concepts with an Application to Preferences in the Babington Smith Model.” International Journal of Approximate Reasoning, vol. 119, no. 2, Elsevier, 2020, pp. 373–407, doi:https://doi.org/10.1016/j.ijar.2020.01.007.","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={https://doi.org/10.1016/j.ijar.2020.01.007}, number={2}, journal={International Journal of Approximate Reasoning}, publisher={Elsevier}, author={Haddenhorst, Björn and Hüllermeier, Eyke and Kolb, Martin}, year={2020}, pages={373–407} }","ama":"Haddenhorst B, Hüllermeier E, Kolb M. Generalized transitivity: A systematic comparison of concepts with an application to preferences in the Babington Smith model. International Journal of Approximate Reasoning. 2020;119(2):373-407. doi:https://doi.org/10.1016/j.ijar.2020.01.007","apa":"Haddenhorst, B., Hüllermeier, E., & Kolb, M. (2020). Generalized transitivity: A systematic comparison of concepts with an application to preferences in the Babington Smith model. International Journal of Approximate Reasoning, 119(2), 373–407. https://doi.org/10.1016/j.ijar.2020.01.007","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.” International Journal of Approximate Reasoning 119, no. 2 (2020): 373–407. https://doi.org/10.1016/j.ijar.2020.01.007."},"type":"journal_article","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."}],"user_id":"85821","publication":"International Journal of Approximate Reasoning","author":[{"first_name":"Björn","full_name":"Haddenhorst, Björn","last_name":"Haddenhorst"},{"last_name":"Hüllermeier","first_name":"Eyke","full_name":"Hüllermeier, Eyke"},{"id":"48880","last_name":"Kolb","full_name":"Kolb, Martin","first_name":"Martin"}],"publisher":"Elsevier","volume":119,"date_created":"2022-09-12T07:13:19Z","status":"public"},{"page":"1753-1783","citation":{"short":"M. Kolb, M. Liesenfeld, Annales Henri Poincaré 20 (2019) 1753–1783.","ieee":"M. Kolb and M. Liesenfeld, “Stochastic Spikes and Poisson Approximation of One-Dimensional Stochastic Differential Equations with Applications to Continuously Measured Quantum Systems,” Annales Henri Poincaré, vol. 20, no. 6, pp. 1753–1783, 2019, doi: http://dx.doi.org/10.1007/s00023-019-00772-9.","chicago":"Kolb, Martin, and Matthias Liesenfeld. “Stochastic Spikes and Poisson Approximation of One-Dimensional Stochastic Differential Equations with Applications to Continuously Measured Quantum Systems.” Annales Henri Poincaré 20, no. 6 (2019): 1753–83. http://dx.doi.org/10.1007/s00023-019-00772-9.","apa":"Kolb, M., & Liesenfeld, M. (2019). Stochastic Spikes and Poisson Approximation of One-Dimensional Stochastic Differential Equations with Applications to Continuously Measured Quantum Systems. Annales Henri Poincaré, 20(6), 1753–1783. http://dx.doi.org/10.1007/s00023-019-00772-9","ama":"Kolb M, Liesenfeld M. Stochastic Spikes and Poisson Approximation of One-Dimensional Stochastic Differential Equations with Applications to Continuously Measured Quantum Systems. Annales Henri Poincaré. 2019;20(6):1753-1783. doi:http://dx.doi.org/10.1007/s00023-019-00772-9","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={http://dx.doi.org/10.1007/s00023-019-00772-9}, number={6}, journal={Annales Henri Poincaré}, publisher={Institute Henri Poincaré}, author={Kolb, Martin and Liesenfeld, Matthias}, year={2019}, pages={1753–1783} }","mla":"Kolb, Martin, and Matthias Liesenfeld. “Stochastic Spikes and Poisson Approximation of One-Dimensional Stochastic Differential Equations with Applications to Continuously Measured Quantum Systems.” Annales Henri Poincaré, vol. 20, no. 6, Institute Henri Poincaré, 2019, pp. 1753–83, doi:http://dx.doi.org/10.1007/s00023-019-00772-9."},"year":"2019","type":"journal_article","issue":"6","_id":"33331","intvolume":" 20","volume":20,"date_created":"2022-09-12T07:18:58Z","status":"public","publication":"Annales Henri Poincaré","publisher":"Institute Henri Poincaré","author":[{"last_name":"Kolb","id":"48880","first_name":"Martin","full_name":"Kolb, Martin"},{"last_name":"Liesenfeld","first_name":"Matthias","full_name":"Liesenfeld, Matthias"}],"user_id":"85821","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."}],"language":[{"iso":"eng"}],"doi":"http://dx.doi.org/10.1007/s00023-019-00772-9","date_updated":"2022-09-12T07:19:02Z","publication_status":"published","department":[{"_id":"96"}],"title":"Stochastic Spikes and Poisson Approximation of One-Dimensional Stochastic Differential Equations with Applications to Continuously Measured Quantum Systems"},{"department":[{"_id":"96"}],"publication":"The Annals of Applied Probability","author":[{"last_name":"Wang","full_name":"Wang, Andi Q.","first_name":"Andi Q."},{"full_name":"Kolb, Martin","first_name":"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"}],"volume":29,"date_created":"2022-09-12T07:24:52Z","status":"public","title":"Theoretical properties of quasi-stationary Monte Carlo methods","user_id":"85821","type":"journal_article","year":"2019","citation":{"bibtex":"@article{Wang_Kolb_Roberts_Steinsaltz_2019, title={Theoretical properties of quasi-stationary Monte Carlo methods}, volume={29}, DOI={http://dx.doi.org/10.1214/18-AAP1422}, number={1}, journal={The Annals of Applied Probability}, author={Wang, Andi Q. and Kolb, Martin and Roberts, Gareth O. and Steinsaltz, David}, year={2019} }","mla":"Wang, Andi Q., et al. “Theoretical Properties of Quasi-Stationary Monte Carlo Methods.” The Annals of Applied Probability, vol. 29, no. 1, 2019, doi:http://dx.doi.org/10.1214/18-AAP1422.","chicago":"Wang, Andi Q., Martin Kolb, Gareth O. Roberts, and David Steinsaltz. “Theoretical Properties of Quasi-Stationary Monte Carlo Methods.” The Annals of Applied Probability 29, no. 1 (2019). http://dx.doi.org/10.1214/18-AAP1422.","ama":"Wang AQ, Kolb M, Roberts GO, Steinsaltz D. Theoretical properties of quasi-stationary Monte Carlo methods. The Annals of Applied Probability. 2019;29(1). doi:http://dx.doi.org/10.1214/18-AAP1422","apa":"Wang, A. Q., Kolb, M., Roberts, G. O., & Steinsaltz, D. (2019). Theoretical properties of quasi-stationary Monte Carlo methods. The Annals of Applied Probability, 29(1). http://dx.doi.org/10.1214/18-AAP1422","ieee":"A. Q. Wang, M. Kolb, G. O. Roberts, and D. Steinsaltz, “Theoretical properties of quasi-stationary Monte Carlo methods,” The Annals of Applied Probability, vol. 29, no. 1, 2019, doi: http://dx.doi.org/10.1214/18-AAP1422.","short":"A.Q. Wang, M. Kolb, G.O. Roberts, D. Steinsaltz, The Annals of Applied Probability 29 (2019)."},"language":[{"iso":"eng"}],"date_updated":"2022-09-12T07:32:35Z","_id":"33333","intvolume":" 29","doi":"http://dx.doi.org/10.1214/18-AAP1422","issue":"1"},{"language":[{"iso":"eng"}],"doi":"http://dx.doi.org/10.1016/j.spa.2018.05.012","date_updated":"2022-09-12T07:46:47Z","publication_status":"published","department":[{"_id":"96"}],"title":"Quasistationary distributions for one-dimensional diffusions with two singular boundary points","citation":{"ieee":"A. Hening and M. Kolb, “Quasistationary distributions for one-dimensional diffusions with two singular boundary points,” Stochastic Processes and their Applications, vol. 129, no. 5, pp. 1659–1696, 2019, doi: http://dx.doi.org/10.1016/j.spa.2018.05.012.","short":"A. Hening, M. Kolb, Stochastic Processes and Their Applications 129 (2019) 1659–1696.","mla":"Hening, Alexandru, and Martin Kolb. “Quasistationary Distributions for One-Dimensional Diffusions with Two Singular Boundary Points.” Stochastic Processes and Their Applications, vol. 129, no. 5, Bernoulli Society for Mathematical Statistics and Probability, 2019, pp. 1659–96, doi:http://dx.doi.org/10.1016/j.spa.2018.05.012.","bibtex":"@article{Hening_Kolb_2019, title={Quasistationary distributions for one-dimensional diffusions with two singular boundary points}, volume={129}, DOI={http://dx.doi.org/10.1016/j.spa.2018.05.012}, 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} }","apa":"Hening, A., & Kolb, M. (2019). Quasistationary distributions for one-dimensional diffusions with two singular boundary points. Stochastic Processes and Their Applications, 129(5), 1659–1696. http://dx.doi.org/10.1016/j.spa.2018.05.012","ama":"Hening A, Kolb M. Quasistationary distributions for one-dimensional diffusions with two singular boundary points. Stochastic Processes and their Applications. 2019;129(5):1659-1696. doi:http://dx.doi.org/10.1016/j.spa.2018.05.012","chicago":"Hening, Alexandru, and Martin Kolb. “Quasistationary Distributions for One-Dimensional Diffusions with Two Singular Boundary Points.” Stochastic Processes and Their Applications 129, no. 5 (2019): 1659–96. http://dx.doi.org/10.1016/j.spa.2018.05.012."},"year":"2019","type":"journal_article","page":"1659-1696","issue":"5","intvolume":" 129","_id":"33334","status":"public","date_created":"2022-09-12T07:46:44Z","volume":129,"publisher":"Bernoulli Society for Mathematical Statistics and Probability","author":[{"last_name":"Hening","full_name":"Hening, Alexandru","first_name":"Alexandru"},{"first_name":"Martin","full_name":"Kolb, Martin","last_name":"Kolb"}],"publication":"Stochastic Processes and their Applications","user_id":"85821","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)."}]},{"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 0Journal of Theoretical Probability 33 (2018): 65–102. https://link.springer.com/article/10.1007/s10959-018-0850-0.","apa":"Hinrichs, G., Kolb, M., & Wachtel, V. (2018). Persistence of one-dimensional AR(1)-processes. Journal of Theoretical Probability, 33, 65–102. https://link.springer.com/article/10.1007/s10959-018-0850-0","ama":"Hinrichs G, Kolb M, Wachtel V. Persistence of one-dimensional AR(1)-processes. Journal of Theoretical Probability. 2018;33:65–102. doi:https://link.springer.com/article/10.1007/s10959-018-0850-0","mla":"Hinrichs, Günter, et al. “Persistence of One-Dimensional AR(1)-Processes.” Journal of Theoretical Probability, vol. 33, Springer Science + Business Media, 2018, pp. 65–102, doi:https://link.springer.com/article/10.1007/s10959-018-0850-0.","bibtex":"@article{Hinrichs_Kolb_Wachtel_2018, title={Persistence of one-dimensional AR(1)-processes}, volume={33}, DOI={https://link.springer.com/article/10.1007/s10959-018-0850-0}, journal={Journal of Theoretical Probability}, publisher={Springer Science + Business Media}, author={Hinrichs, Günter and Kolb, Martin and Wachtel, Vitali}, year={2018}, pages={65–102} }","short":"G. Hinrichs, M. Kolb, V. Wachtel, Journal of Theoretical Probability 33 (2018) 65–102.","ieee":"G. Hinrichs, M. Kolb, and V. Wachtel, “Persistence of one-dimensional AR(1)-processes,” Journal of Theoretical Probability, vol. 33, pp. 65–102, 2018, doi: https://link.springer.com/article/10.1007/s10959-018-0850-0."},"year":"2018","page":"65–102"},{"volume":108,"publication_status":"published","date_created":"2022-09-12T08:08:05Z","status":"public","publication":"Letters in Mathematical Physics","department":[{"_id":"96"}],"author":[{"last_name":"Boßmann","full_name":"Boßmann, Lea","first_name":"Lea"},{"last_name":"Grummt","first_name":"Robert","full_name":"Grummt, Robert"},{"full_name":"Kolb, Martin","first_name":"Martin","id":"48880","last_name":"Kolb"}],"title":"On the dipole approximation with error estimates","user_id":"85821","abstract":[{"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.","lang":"eng"}],"page":"185–193","year":"2017","type":"journal_article","citation":{"chicago":"Boßmann, Lea, Robert Grummt, and Martin Kolb. “On the Dipole Approximation with Error Estimates.” Letters in Mathematical Physics 108 (2017): 185–193. https://link.springer.com/article/10.1007/s11005-017-0999-y.","apa":"Boßmann, L., Grummt, R., & Kolb, M. (2017). On the dipole approximation with error estimates. Letters in Mathematical Physics, 108, 185–193. https://link.springer.com/article/10.1007/s11005-017-0999-y","ama":"Boßmann L, Grummt R, Kolb M. On the dipole approximation with error estimates. Letters in Mathematical Physics. 2017;108:185–193. doi:https://link.springer.com/article/10.1007/s11005-017-0999-y","mla":"Boßmann, Lea, et al. “On the Dipole Approximation with Error Estimates.” Letters in Mathematical Physics, vol. 108, 2017, pp. 185–193, doi:https://link.springer.com/article/10.1007/s11005-017-0999-y.","bibtex":"@article{Boßmann_Grummt_Kolb_2017, title={On the dipole approximation with error estimates}, volume={108}, DOI={https://link.springer.com/article/10.1007/s11005-017-0999-y}, journal={Letters in Mathematical Physics}, author={Boßmann, Lea and Grummt, Robert and Kolb, Martin}, year={2017}, pages={185–193} }","short":"L. Boßmann, R. Grummt, M. Kolb, Letters in Mathematical Physics 108 (2017) 185–193.","ieee":"L. Boßmann, R. Grummt, and M. Kolb, “On the dipole approximation with error estimates,” Letters in Mathematical Physics, vol. 108, pp. 185–193, 2017, doi: https://link.springer.com/article/10.1007/s11005-017-0999-y."},"language":[{"iso":"eng"}],"doi":"https://link.springer.com/article/10.1007/s11005-017-0999-y","date_updated":"2022-09-12T08:08:09Z","_id":"33336","intvolume":" 108"},{"title":"Conditional survival distributions of Brownian trajectories in a one dimensional Poissonian environment in the critical case","user_id":"85821","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]."}],"publication_status":"published","volume":22,"status":"public","date_created":"2022-09-13T07:47:39Z","author":[{"last_name":"Savov","first_name":"Mladen","full_name":"Savov, Mladen"},{"first_name":"Martin","full_name":"Kolb, Martin","last_name":"Kolb","id":"48880"}],"publisher":" Institute of Mathematical Statistics & Bernoulli Society","department":[{"_id":"96"}],"publication":"Electronic Journal of Probability","doi":"https://doi.org/10.1214/17-EJP4468","_id":"33342","date_updated":"2022-09-13T07:47:46Z","intvolume":" 22","type":"journal_article","citation":{"ieee":"M. Savov and M. Kolb, “Conditional survival distributions of Brownian trajectories in a one dimensional Poissonian environment in the critical case,” Electronic Journal of Probability, vol. 22, 2017, doi: https://doi.org/10.1214/17-EJP4468.","short":"M. Savov, M. Kolb, Electronic Journal of Probability 22 (2017).","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={https://doi.org/10.1214/17-EJP4468}, journal={Electronic Journal of Probability}, publisher={ Institute of Mathematical Statistics & Bernoulli Society}, author={Savov, Mladen and Kolb, Martin}, year={2017} }","mla":"Savov, Mladen, and Martin Kolb. “Conditional Survival Distributions of Brownian Trajectories in a One Dimensional Poissonian Environment in the Critical Case.” Electronic Journal of Probability, vol. 22, Institute of Mathematical Statistics & Bernoulli Society, 2017, doi:https://doi.org/10.1214/17-EJP4468.","ama":"Savov M, Kolb M. Conditional survival distributions of Brownian trajectories in a one dimensional Poissonian environment in the critical case. Electronic Journal of Probability. 2017;22. doi:https://doi.org/10.1214/17-EJP4468","apa":"Savov, M., & Kolb, M. (2017). Conditional survival distributions of Brownian trajectories in a one dimensional Poissonian environment in the critical case. Electronic Journal of Probability, 22. https://doi.org/10.1214/17-EJP4468","chicago":"Savov, Mladen, and Martin Kolb. “Conditional Survival Distributions of Brownian Trajectories in a One Dimensional Poissonian Environment in the Critical Case.” Electronic Journal of Probability 22 (2017). https://doi.org/10.1214/17-EJP4468."},"year":"2017","language":[{"iso":"eng"}]},{"doi":"https://link.springer.com/content/pdf/10.1007/s00209-016-1677-y.pdf","_id":"33343","date_updated":"2022-09-13T07:56:59Z","intvolume":" 284","citation":{"short":"M. Kolb, D. Krejčiřík, Mathematische Zeitschrift 284 (2016) 877–900.","ieee":"M. Kolb and D. Krejčiřík, “Spectral analysis of the diffusion operator with random jumps from the boundary,” Mathematische Zeitschrift, vol. 284, pp. 877–900, 2016, doi: https://link.springer.com/content/pdf/10.1007/s00209-016-1677-y.pdf.","ama":"Kolb M, Krejčiřík D. Spectral analysis of the diffusion operator with random jumps from the boundary. Mathematische Zeitschrift. 2016;284:877-900. doi:https://link.springer.com/content/pdf/10.1007/s00209-016-1677-y.pdf","apa":"Kolb, M., & Krejčiřík, D. (2016). Spectral analysis of the diffusion operator with random jumps from the boundary. Mathematische Zeitschrift, 284, 877–900. https://link.springer.com/content/pdf/10.1007/s00209-016-1677-y.pdf","chicago":"Kolb, Martin, and David Krejčiřík. “Spectral Analysis of the Diffusion Operator with Random Jumps from the Boundary.” Mathematische Zeitschrift 284 (2016): 877–900. https://link.springer.com/content/pdf/10.1007/s00209-016-1677-y.pdf.","mla":"Kolb, Martin, and David Krejčiřík. “Spectral Analysis of the Diffusion Operator with Random Jumps from the Boundary.” Mathematische Zeitschrift, vol. 284, Springer, 2016, pp. 877–900, doi:https://link.springer.com/content/pdf/10.1007/s00209-016-1677-y.pdf.","bibtex":"@article{Kolb_Krejčiřík_2016, title={Spectral analysis of the diffusion operator with random jumps from the boundary}, volume={284}, DOI={https://link.springer.com/content/pdf/10.1007/s00209-016-1677-y.pdf}, journal={Mathematische Zeitschrift}, publisher={Springer}, author={Kolb, Martin and Krejčiřík, David}, year={2016}, pages={877–900} }"},"year":"2016","type":"journal_article","page":"877-900","language":[{"iso":"eng"}],"title":"Spectral analysis of the diffusion operator with random jumps from the boundary","user_id":"85821","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."}],"publication_status":"published","volume":284,"status":"public","date_created":"2022-09-13T07:56:56Z","publisher":"Springer","author":[{"first_name":"Martin","full_name":"Kolb, Martin","last_name":"Kolb","id":"48880"},{"first_name":"David","full_name":"Krejčiřík, David","last_name":"Krejčiřík"}],"department":[{"_id":"96"}],"publication":"Mathematische Zeitschrift"},{"language":[{"iso":"eng"}],"page":"1077-1099","year":"2016","type":"journal_article","citation":{"chicago":"Richthammer, Thomas. “Lower Bound on the Mean Square Displacement of Particles in the Hard Disk Model.” Communications in Mathematical Physics 345 (2016): 1077–99. https://link.springer.com/article/10.1007/s00220-016-2584-0.","ama":"Richthammer T. Lower Bound on the Mean Square Displacement of Particles in the Hard Disk Model. Communications in Mathematical Physics . 2016;345:1077-1099. doi:https://link.springer.com/article/10.1007/s00220-016-2584-0","apa":"Richthammer, T. (2016). Lower Bound on the Mean Square Displacement of Particles in the Hard Disk Model. Communications in Mathematical Physics , 345, 1077–1099. https://link.springer.com/article/10.1007/s00220-016-2584-0","mla":"Richthammer, Thomas. “Lower Bound on the Mean Square Displacement of Particles in the Hard Disk Model.” Communications in Mathematical Physics , vol. 345, 2016, pp. 1077–99, doi:https://link.springer.com/article/10.1007/s00220-016-2584-0.","bibtex":"@article{Richthammer_2016, title={Lower Bound on the Mean Square Displacement of Particles in the Hard Disk Model}, volume={345}, DOI={https://link.springer.com/article/10.1007/s00220-016-2584-0}, journal={Communications in Mathematical Physics }, author={Richthammer, Thomas}, year={2016}, pages={1077–1099} }","short":"T. Richthammer, Communications in Mathematical Physics 345 (2016) 1077–1099.","ieee":"T. Richthammer, “Lower Bound on the Mean Square Displacement of Particles in the Hard Disk Model,” Communications in Mathematical Physics , vol. 345, pp. 1077–1099, 2016, doi: https://link.springer.com/article/10.1007/s00220-016-2584-0."},"date_updated":"2022-09-13T08:01:36Z","_id":"33344","intvolume":" 345","doi":"https://link.springer.com/article/10.1007/s00220-016-2584-0","publication":"Communications in Mathematical Physics ","department":[{"_id":"96"}],"author":[{"full_name":"Richthammer, Thomas","first_name":"Thomas","id":"62054","last_name":"Richthammer"}],"date_created":"2022-09-13T08:01:29Z","status":"public","volume":345,"publication_status":"published","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."}],"user_id":"85821","title":"Lower Bound on the Mean Square Displacement of Particles in the Hard Disk Model"},{"language":[{"iso":"eng"}],"year":"2016","citation":{"short":"M. Kolb, M. Savov, The Annals of Probability 44 (2016).","ieee":"M. Kolb and M. Savov, “Transience and recurrence of a Brownian path with limited local time,” The Annals of Probability, vol. 44, no. 6, 2016, doi: http://dx.doi.org/10.1214/15-AOP1069.","chicago":"Kolb, Martin, and Mladen Savov. “Transience and Recurrence of a Brownian Path with Limited Local Time.” The Annals of Probability 44, no. 6 (2016). http://dx.doi.org/10.1214/15-AOP1069.","apa":"Kolb, M., & Savov, M. (2016). Transience and recurrence of a Brownian path with limited local time. The Annals of Probability, 44(6). http://dx.doi.org/10.1214/15-AOP1069","ama":"Kolb M, Savov M. Transience and recurrence of a Brownian path with limited local time. The Annals of Probability. 2016;44(6). doi:http://dx.doi.org/10.1214/15-AOP1069","bibtex":"@article{Kolb_Savov_2016, title={Transience and recurrence of a Brownian path with limited local time}, volume={44}, DOI={http://dx.doi.org/10.1214/15-AOP1069}, number={6}, journal={The Annals of Probability}, publisher={Institute of Mathematical Statistics}, author={Kolb, Martin and Savov, Mladen}, year={2016} }","mla":"Kolb, Martin, and Mladen Savov. “Transience and Recurrence of a Brownian Path with Limited Local Time.” The Annals of Probability, vol. 44, no. 6, Institute of Mathematical Statistics, 2016, doi:http://dx.doi.org/10.1214/15-AOP1069."},"type":"journal_article","intvolume":" 44","_id":"33357","date_updated":"2022-09-14T04:22:26Z","issue":"6","doi":"http://dx.doi.org/10.1214/15-AOP1069","department":[{"_id":"96"}],"publication":"The Annals of Probability","publisher":"Institute of Mathematical Statistics","author":[{"full_name":"Kolb, Martin","first_name":"Martin","id":"48880","last_name":"Kolb"},{"full_name":"Savov, Mladen","first_name":"Mladen","last_name":"Savov"}],"date_created":"2022-09-14T04:22:23Z","status":"public","publication_status":"published","volume":44,"abstract":[{"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. ","lang":"eng"}],"user_id":"85821","title":"Transience and recurrence of a Brownian path with limited local time"},{"abstract":[{"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. ","lang":"eng"}],"user_id":"85821","author":[{"last_name":"Richthammer","id":"62054","first_name":"Thomas","full_name":"Richthammer, Thomas"},{"full_name":"Biskup, Marek","first_name":"Marek","last_name":"Biskup"}],"publisher":"Springer Science+Business Media","publication":"Communications in Mathematical Physics","volume":25,"status":"public","date_created":"2022-09-14T04:57:58Z","_id":"33359","intvolume":" 25","issue":"2","year":"2015","citation":{"apa":"Richthammer, T., & Biskup, M. (2015). Gibbs measures on permutations over one-dimensional discrete point sets. Communications in Mathematical Physics, 25(2), 898–929. https://doi.org/10.48550/arXiv.1310.0248","ama":"Richthammer T, Biskup M. Gibbs measures on permutations over one-dimensional discrete point sets. Communications in Mathematical Physics. 2015;25(2):898-929. doi:https://doi.org/10.48550/arXiv.1310.0248","chicago":"Richthammer, Thomas, and Marek Biskup. “Gibbs Measures on Permutations over One-Dimensional Discrete Point Sets.” Communications in Mathematical Physics 25, no. 2 (2015): 898–929. https://doi.org/10.48550/arXiv.1310.0248.","mla":"Richthammer, Thomas, and Marek Biskup. “Gibbs Measures on Permutations over One-Dimensional Discrete Point Sets.” Communications in Mathematical Physics, vol. 25, no. 2, Springer Science+Business Media, 2015, pp. 898–929, doi:https://doi.org/10.48550/arXiv.1310.0248.","bibtex":"@article{Richthammer_Biskup_2015, title={Gibbs measures on permutations over one-dimensional discrete point sets}, volume={25}, DOI={https://doi.org/10.48550/arXiv.1310.0248}, number={2}, journal={Communications in Mathematical Physics}, publisher={Springer Science+Business Media}, author={Richthammer, Thomas and Biskup, Marek}, year={2015}, pages={898–929} }","short":"T. Richthammer, M. Biskup, Communications in Mathematical Physics 25 (2015) 898–929.","ieee":"T. Richthammer and M. Biskup, “Gibbs measures on permutations over one-dimensional discrete point sets,” Communications in Mathematical Physics, vol. 25, no. 2, pp. 898–929, 2015, doi: https://doi.org/10.48550/arXiv.1310.0248."},"type":"journal_article","page":"898-929","title":"Gibbs measures on permutations over one-dimensional discrete point sets","department":[{"_id":"96"}],"publication_status":"published","date_updated":"2022-09-14T04:58:02Z","doi":"https://doi.org/10.48550/arXiv.1310.0248","language":[{"iso":"eng"}]},{"publication_status":"published","department":[{"_id":"96"}],"title":"The rate of convergence to stationarity for M/G/1 models with admission controls via coupling","language":[{"iso":"eng"}],"doi":"http://dx.doi.org/10.1080/15326349.2015.1090322","date_updated":"2022-09-14T04:52:19Z","volume":32,"status":"public","date_created":"2022-09-14T04:52:15Z","author":[{"id":"48880","last_name":"Kolb","full_name":"Kolb, Martin","first_name":"Martin"},{"first_name":"Wolfgang","full_name":"Stadje, Wolfgang","last_name":"Stadje"},{"last_name":"Wübker","full_name":"Wübker, Achim","first_name":"Achim"}],"publisher":"INFORMS","publication":"Stochastic Models","user_id":"85821","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."}],"type":"journal_article","citation":{"chicago":"Kolb, Martin, Wolfgang Stadje, and Achim Wübker. “The Rate of Convergence to Stationarity for M/G/1 Models with Admission Controls via Coupling.” Stochastic Models 32, no. 1 (2015): 121–35. http://dx.doi.org/10.1080/15326349.2015.1090322.","ama":"Kolb M, Stadje W, Wübker A. The rate of convergence to stationarity for M/G/1 models with admission controls via coupling. Stochastic Models. 2015;32(1):121-135. doi:http://dx.doi.org/10.1080/15326349.2015.1090322","apa":"Kolb, M., Stadje, W., & Wübker, A. (2015). The rate of convergence to stationarity for M/G/1 models with admission controls via coupling. Stochastic Models, 32(1), 121–135. http://dx.doi.org/10.1080/15326349.2015.1090322","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={http://dx.doi.org/10.1080/15326349.2015.1090322}, number={1}, journal={Stochastic Models}, publisher={INFORMS}, author={Kolb, Martin and Stadje, Wolfgang and Wübker, Achim}, year={2015}, pages={121–135} }","mla":"Kolb, Martin, et al. “The Rate of Convergence to Stationarity for M/G/1 Models with Admission Controls via Coupling.” Stochastic Models, vol. 32, no. 1, INFORMS, 2015, pp. 121–35, doi:http://dx.doi.org/10.1080/15326349.2015.1090322.","short":"M. Kolb, W. Stadje, A. Wübker, Stochastic Models 32 (2015) 121–135.","ieee":"M. Kolb, W. Stadje, and A. Wübker, “The rate of convergence to stationarity for M/G/1 models with admission controls via coupling,” Stochastic Models, vol. 32, no. 1, pp. 121–135, 2015, doi: http://dx.doi.org/10.1080/15326349.2015.1090322."},"year":"2015","page":"121-135","issue":"1","_id":"33358","intvolume":" 32"},{"language":[{"iso":"eng"}],"page":"495-513","type":"journal_article","citation":{"short":"M. Kolb, D. Denisov, V. Wachtel, Journal of the London Mathematical Society 91 (2015) 495–513.","ieee":"M. Kolb, D. Denisov, and V. Wachtel, “Local asymptotics for the area of random walk excursions,” Journal of the London Mathematical Society, vol. 91, no. 2, pp. 495–513, 2015.","apa":"Kolb, M., Denisov, D., & Wachtel, V. (2015). Local asymptotics for the area of random walk excursions. Journal of the London Mathematical Society, 91(2), 495–513.","ama":"Kolb M, Denisov D, Wachtel V. Local asymptotics for the area of random walk excursions. Journal of the London Mathematical Society. 2015;91(2):495-513.","chicago":"Kolb, Martin, Denis Denisov, and Vitali Wachtel. “Local Asymptotics for the Area of Random Walk Excursions.” Journal of the London Mathematical Society 91, no. 2 (2015): 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} }","mla":"Kolb, Martin, et al. “Local Asymptotics for the Area of Random Walk Excursions.” Journal of the London Mathematical Society, vol. 91, no. 2, London Mathematical Society, 2015, pp. 495–513."},"year":"2015","_id":"33360","intvolume":" 91","date_updated":"2022-09-14T05:01:45Z","issue":"2","department":[{"_id":"96"}],"publication":"Journal of the London Mathematical Society","publisher":"London Mathematical Society","author":[{"full_name":"Kolb, Martin","first_name":"Martin","id":"48880","last_name":"Kolb"},{"full_name":"Denisov, Denis","first_name":"Denis","last_name":"Denisov"},{"last_name":"Wachtel","full_name":"Wachtel, Vitali","first_name":"Vitali"}],"date_created":"2022-09-14T05:01:41Z","status":"public","publication_status":"published","volume":91,"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."}],"user_id":"85821","title":"Local asymptotics for the area of random walk excursions"},{"doi":"http://dx.doi.org/10.1214/ECP.v19-3006","date_updated":"2022-09-14T05:15:06Z","language":[{"iso":"eng"}],"title":"Exponential ergodicity of killed Lévy processes in a finite interval","publication_status":"published","department":[{"_id":"96"}],"issue":"31","intvolume":" 19","_id":"33361","page":"1-9","year":"2014","type":"journal_article","citation":{"mla":"Kolb, Martin, and Mladen Savov. “Exponential Ergodicity of Killed Lévy Processes in a Finite Interval.” Electronic Communications in Probability, vol. 19, no. 31, Institute of Mathematical Statistics (IMS), 2014, pp. 1–9, doi:http://dx.doi.org/10.1214/ECP.v19-3006.","bibtex":"@article{Kolb_Savov_2014, title={Exponential ergodicity of killed Lévy processes in a finite interval}, volume={19}, DOI={http://dx.doi.org/10.1214/ECP.v19-3006}, 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.” Electronic Communications in Probability 19, no. 31 (2014): 1–9. http://dx.doi.org/10.1214/ECP.v19-3006.","apa":"Kolb, M., & Savov, M. (2014). Exponential ergodicity of killed Lévy processes in a finite interval. Electronic Communications in Probability, 19(31), 1–9. http://dx.doi.org/10.1214/ECP.v19-3006","ama":"Kolb M, Savov M. Exponential ergodicity of killed Lévy processes in a finite interval. Electronic Communications in Probability. 2014;19(31):1-9. doi:http://dx.doi.org/10.1214/ECP.v19-3006","ieee":"M. Kolb and M. Savov, “Exponential ergodicity of killed Lévy processes in a finite interval,” Electronic Communications in Probability, vol. 19, no. 31, pp. 1–9, 2014, doi: http://dx.doi.org/10.1214/ECP.v19-3006.","short":"M. Kolb, M. Savov, Electronic Communications in Probability 19 (2014) 1–9."},"user_id":"85821","abstract":[{"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.
","lang":"eng"}],"volume":19,"date_created":"2022-09-14T05:15:00Z","status":"public","publication":"Electronic Communications in Probability","publisher":"Institute of Mathematical Statistics (IMS)","author":[{"full_name":"Kolb, Martin","first_name":"Martin","id":"48880","last_name":"Kolb"},{"last_name":"Savov","full_name":"Savov, Mladen","first_name":"Mladen"}]}]