[{"status":"public","type":"journal_article","article_type":"original","article_number":"012220","project":[{"_id":"266","name":"PhoQC: Photonisches Quantencomputing"},{"name":"TRR 142 ; TP: C10: Erzeugung und Charakterisierung von Quantenlicht in nichtlinearen Systemen: Eine theoretische Analyse","_id":"174"}],"_id":"63656","user_id":"99427","department":[{"_id":"799"}],"citation":{"apa":"Ares, L., Pinske, J., Hinrichs, B., Kolb, M., &#38; Sperling, J. (2026). Restricted Monte Carlo wave-function method and Lindblad equation for identifying entangling open-quantum-system dynamics. <i>Physical Review A</i>, <i>113</i>(1), Article 012220. <a href=\"https://doi.org/10.1103/hcj7-8zlg\">https://doi.org/10.1103/hcj7-8zlg</a>","short":"L. Ares, J. Pinske, B. Hinrichs, M. Kolb, J. Sperling, Physical Review A 113 (2026).","mla":"Ares, Laura, et al. “Restricted Monte Carlo Wave-Function Method and Lindblad Equation for Identifying Entangling Open-Quantum-System Dynamics.” <i>Physical Review A</i>, vol. 113, no. 1, 012220, American Physical Society (APS), 2026, doi:<a href=\"https://doi.org/10.1103/hcj7-8zlg\">10.1103/hcj7-8zlg</a>.","bibtex":"@article{Ares_Pinske_Hinrichs_Kolb_Sperling_2026, title={Restricted Monte Carlo wave-function method and Lindblad equation for identifying entangling open-quantum-system dynamics}, volume={113}, DOI={<a href=\"https://doi.org/10.1103/hcj7-8zlg\">10.1103/hcj7-8zlg</a>}, number={1012220}, journal={Physical Review A}, publisher={American Physical Society (APS)}, author={Ares, Laura and Pinske, Julien and Hinrichs, Benjamin and Kolb, Martin and Sperling, Jan}, year={2026} }","ama":"Ares L, Pinske J, Hinrichs B, Kolb M, Sperling J. Restricted Monte Carlo wave-function method and Lindblad equation for identifying entangling open-quantum-system dynamics. <i>Physical Review A</i>. 2026;113(1). doi:<a href=\"https://doi.org/10.1103/hcj7-8zlg\">10.1103/hcj7-8zlg</a>","chicago":"Ares, Laura, Julien Pinske, Benjamin Hinrichs, Martin Kolb, and Jan Sperling. “Restricted Monte Carlo Wave-Function Method and Lindblad Equation for Identifying Entangling Open-Quantum-System Dynamics.” <i>Physical Review A</i> 113, no. 1 (2026). <a href=\"https://doi.org/10.1103/hcj7-8zlg\">https://doi.org/10.1103/hcj7-8zlg</a>.","ieee":"L. Ares, J. Pinske, B. Hinrichs, M. Kolb, and J. Sperling, “Restricted Monte Carlo wave-function method and Lindblad equation for identifying entangling open-quantum-system dynamics,” <i>Physical Review A</i>, vol. 113, no. 1, Art. no. 012220, 2026, doi: <a href=\"https://doi.org/10.1103/hcj7-8zlg\">10.1103/hcj7-8zlg</a>."},"intvolume":"       113","publication_status":"published","publication_identifier":{"issn":["2469-9926","2469-9934"]},"doi":"10.1103/hcj7-8zlg","date_updated":"2026-01-18T18:15:01Z","author":[{"last_name":"Ares","full_name":"Ares, Laura","first_name":"Laura"},{"last_name":"Pinske","full_name":"Pinske, Julien","first_name":"Julien"},{"last_name":"Hinrichs","orcid":"0000-0001-9074-1205","full_name":"Hinrichs, Benjamin","id":"99427","first_name":"Benjamin"},{"last_name":"Kolb","full_name":"Kolb, Martin","id":"48880","first_name":"Martin"},{"first_name":"Jan","id":"75127","full_name":"Sperling, Jan","last_name":"Sperling","orcid":"0000-0002-5844-3205"}],"volume":113,"publication":"Physical Review A","language":[{"iso":"eng"}],"external_id":{"arxiv":["2412.08735"]},"year":"2026","issue":"1","title":"Restricted Monte Carlo wave-function method and Lindblad equation for identifying entangling open-quantum-system dynamics","publisher":"American Physical Society (APS)","date_created":"2026-01-18T18:08:18Z"},{"article_type":"letter_note","article_number":"L010403","department":[{"_id":"799"}],"user_id":"99427","_id":"63657","project":[{"_id":"266","name":"PhoQC: Photonisches Quantencomputing"},{"name":"TRR 142 ; TP: C10: Erzeugung und Charakterisierung von Quantenlicht in nichtlinearen Systemen: Eine theoretische Analyse","_id":"174"}],"status":"public","type":"journal_article","doi":"10.1103/kd3b-bfxq","volume":113,"author":[{"full_name":"Pinske, Julien","last_name":"Pinske","first_name":"Julien"},{"first_name":"Laura","last_name":"Ares","full_name":"Ares, Laura"},{"last_name":"Hinrichs","orcid":"0000-0001-9074-1205","full_name":"Hinrichs, Benjamin","id":"99427","first_name":"Benjamin"},{"full_name":"Kolb, Martin","id":"48880","last_name":"Kolb","first_name":"Martin"},{"first_name":"Jan","last_name":"Sperling","orcid":"0000-0002-5844-3205","full_name":"Sperling, Jan","id":"75127"}],"date_updated":"2026-01-18T18:15:26Z","intvolume":"       113","citation":{"mla":"Pinske, Julien, et al. “Separability Lindblad Equation for Dynamical Open-System Entanglement.” <i>Physical Review A</i>, vol. 113, no. 1, L010403, American Physical Society (APS), 2026, doi:<a href=\"https://doi.org/10.1103/kd3b-bfxq\">10.1103/kd3b-bfxq</a>.","short":"J. Pinske, L. Ares, B. Hinrichs, M. Kolb, J. Sperling, Physical Review A 113 (2026).","bibtex":"@article{Pinske_Ares_Hinrichs_Kolb_Sperling_2026, title={Separability Lindblad equation for dynamical open-system entanglement}, volume={113}, DOI={<a href=\"https://doi.org/10.1103/kd3b-bfxq\">10.1103/kd3b-bfxq</a>}, number={1L010403}, journal={Physical Review A}, publisher={American Physical Society (APS)}, author={Pinske, Julien and Ares, Laura and Hinrichs, Benjamin and Kolb, Martin and Sperling, Jan}, year={2026} }","apa":"Pinske, J., Ares, L., Hinrichs, B., Kolb, M., &#38; Sperling, J. (2026). Separability Lindblad equation for dynamical open-system entanglement. <i>Physical Review A</i>, <i>113</i>(1), Article L010403. <a href=\"https://doi.org/10.1103/kd3b-bfxq\">https://doi.org/10.1103/kd3b-bfxq</a>","ama":"Pinske J, Ares L, Hinrichs B, Kolb M, Sperling J. Separability Lindblad equation for dynamical open-system entanglement. <i>Physical Review A</i>. 2026;113(1). doi:<a href=\"https://doi.org/10.1103/kd3b-bfxq\">10.1103/kd3b-bfxq</a>","chicago":"Pinske, Julien, Laura Ares, Benjamin Hinrichs, Martin Kolb, and Jan Sperling. “Separability Lindblad Equation for Dynamical Open-System Entanglement.” <i>Physical Review A</i> 113, no. 1 (2026). <a href=\"https://doi.org/10.1103/kd3b-bfxq\">https://doi.org/10.1103/kd3b-bfxq</a>.","ieee":"J. Pinske, L. Ares, B. Hinrichs, M. Kolb, and J. Sperling, “Separability Lindblad equation for dynamical open-system entanglement,” <i>Physical Review A</i>, vol. 113, no. 1, Art. no. L010403, 2026, doi: <a href=\"https://doi.org/10.1103/kd3b-bfxq\">10.1103/kd3b-bfxq</a>."},"publication_identifier":{"issn":["2469-9926","2469-9934"]},"publication_status":"published","language":[{"iso":"eng"}],"external_id":{"arxiv":["2412.08724"]},"publication":"Physical Review A","title":"Separability Lindblad equation for dynamical open-system entanglement","date_created":"2026-01-18T18:11:27Z","publisher":"American Physical Society (APS)","year":"2026","issue":"1"},{"publication_status":"published","issue":"4","year":"2022","citation":{"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.","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.","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} }","short":"M. Kolb, A. Klump, Theory of Probability and Its Applications 67 (2022) 717–744.","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."},"page":"717-744","intvolume":"        67","date_updated":"2023-01-10T08:13:30Z","publisher":"Society for Industrial and Applied Mathematics","author":[{"last_name":"Kolb","id":"48880","full_name":"Kolb, Martin","first_name":"Martin"},{"full_name":"Klump, Alexander","id":"45067","last_name":"Klump","first_name":"Alexander"}],"date_created":"2023-01-10T08:13:17Z","volume":67,"title":"Uniqueness of the Inverse First Passage Time Problem and the Shape of the Shiryaev boundary","type":"journal_article","publication":"Theory of Probability and its Applications","status":"public","_id":"35644","user_id":"85821","department":[{"_id":"96"}],"language":[{"iso":"eng"}]},{"publication_status":"published","issue":"27","year":"2022","page":"1-28","citation":{"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>.","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>.","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>","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>.","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} }","short":"M. Kolb, M. Liesenfeld, Electronic Journal of Probability (2022) 1–28.","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>"},"date_updated":"2023-01-10T08:19:38Z","publisher":"Institute of Mathematical Statistics","author":[{"last_name":"Kolb","id":"48880","full_name":"Kolb, Martin","first_name":"Martin"},{"last_name":"Liesenfeld","full_name":"Liesenfeld, Matthias","first_name":"Matthias"}],"date_created":"2023-01-10T08:19:25Z","title":"On non-extinction in a Fleming-Viot-type particle model with Bessel drift","doi":"https://doi.org/10.1214/22-EJP866","publication":"Electronic Journal of Probability","type":"journal_article","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"}],"status":"public","_id":"35649","department":[{"_id":"96"}],"user_id":"85821","language":[{"iso":"eng"}]},{"type":"journal_article","publication":"Electronic Journal of Probability","status":"public","abstract":[{"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.","lang":"eng"}],"user_id":"85821","department":[{"_id":"96"}],"_id":"35650","language":[{"iso":"eng"}],"publication_status":"published","citation":{"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} }","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.","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>","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>.","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>"},"page":"1-43","intvolume":"        27","year":"2022","author":[{"first_name":"Denis","full_name":"Denisov, Denis","last_name":"Denisov"},{"last_name":"Hinrichs","full_name":"Hinrichs, Günter","first_name":"Günter"},{"last_name":"Kolb","id":"48880","full_name":"Kolb, Martin","first_name":"Martin"},{"last_name":"Wachtel","full_name":"Wachtel, Vitali","first_name":"Vitali"}],"date_created":"2023-01-10T08:28:12Z","volume":27,"publisher":"Institute of Mathematical Statistics","date_updated":"2023-01-10T08:29:02Z","doi":"https://doi.org/10.48550/arXiv.2203.14772","title":"Persistence of autoregressive sequences with logarithmic tails"},{"user_id":"85821","department":[{"_id":"96"}],"_id":"33278","type":"journal_article","status":"public","author":[{"first_name":"Martin","id":"48880","full_name":"Kolb, Martin","last_name":"Kolb"},{"first_name":"Tobias","full_name":"Weich, Tobias","last_name":"Weich"},{"last_name":"Wolf","full_name":"Wolf, Lasse","first_name":"Lasse"}],"volume":23,"oa":"1","date_updated":"2022-09-08T06:06:13Z","main_file_link":[{"open_access":"1","url":"https://link.springer.com/article/10.1007/s00023-021-01121-5"}],"related_material":{"link":[{"relation":"contains","url":"https://link.springer.com/article/10.1007/s00023-021-01121-5"}]},"publication_status":"published","citation":{"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.","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.","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} }","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.","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.","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."},"intvolume":"        23","page":"1283-1296","language":[{"iso":"eng"}],"publication":"Annales Henri Poincaré ","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."}],"date_created":"2022-09-07T07:05:33Z","publisher":"Springer Science + Business Media","title":"Spectral Asymptotics for Kinetic Brownian Motion on Surfaces of Constant Curvature","issue":"4","year":"2021"},{"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>","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>.","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} }","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."},"page":"1453-1472","intvolume":"        26","year":"2020","issue":"2","publication_status":"published","doi":"https://doi.org/10.48550/arXiv.1903.03792","title":"A Characterization of the Finiteness of Perpetual Integrals of Levy Processes","date_created":"2022-09-08T06:36:37Z","author":[{"first_name":"Martin","id":"48880","full_name":"Kolb, Martin","last_name":"Kolb"},{"first_name":"Mladen","full_name":"Savov, Mladen","last_name":"Savov"}],"volume":26,"date_updated":"2022-09-08T06:48:40Z","publisher":"Bernoulli Society for Mathematical Statistics and Probability","status":"public","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)."}],"type":"journal_article","publication":"Bernoulli","language":[{"iso":"eng"}],"keyword":["L ́evy processes","Perpetual integrals","Potential measures"],"user_id":"85821","department":[{"_id":"96"}],"_id":"33282"},{"type":"journal_article","publication":"International Journal of Approximate Reasoning","status":"public","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","department":[{"_id":"96"}],"_id":"33330","language":[{"iso":"eng"}],"issue":"2","publication_status":"published","citation":{"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} }","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.","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>","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>","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>.","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>."},"page":"373-407","intvolume":"       119","year":"2020","author":[{"last_name":"Haddenhorst","full_name":"Haddenhorst, Björn","first_name":"Björn"},{"first_name":"Eyke","last_name":"Hüllermeier","full_name":"Hüllermeier, Eyke"},{"full_name":"Kolb, Martin","id":"48880","last_name":"Kolb","first_name":"Martin"}],"date_created":"2022-09-12T07:13:19Z","volume":119,"publisher":"Elsevier","date_updated":"2022-09-12T07:13:30Z","doi":"https://doi.org/10.1016/j.ijar.2020.01.007","title":"Generalized transitivity: A systematic comparison of concepts with an application to preferences in the Babington Smith model"},{"volume":20,"date_created":"2022-09-12T07:18:58Z","author":[{"last_name":"Kolb","id":"48880","full_name":"Kolb, Martin","first_name":"Martin"},{"last_name":"Liesenfeld","full_name":"Liesenfeld, Matthias","first_name":"Matthias"}],"publisher":"Institute Henri Poincaré","date_updated":"2022-09-12T07:19:02Z","doi":"http://dx.doi.org/10.1007/s00023-019-00772-9","title":"Stochastic Spikes and Poisson Approximation of One-Dimensional Stochastic Differential Equations with Applications to Continuously Measured Quantum Systems","issue":"6","publication_status":"published","page":"1753-1783","intvolume":"        20","citation":{"short":"M. Kolb, M. Liesenfeld, Annales Henri Poincaré 20 (2019) 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.” <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>.","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} }","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>","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>","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>."},"year":"2019","department":[{"_id":"96"}],"user_id":"85821","_id":"33331","language":[{"iso":"eng"}],"publication":"Annales Henri Poincaré","type":"journal_article","status":"public","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."}]},{"status":"public","publication":"The Annals of Applied Probability","type":"journal_article","language":[{"iso":"eng"}],"_id":"33333","department":[{"_id":"96"}],"user_id":"85821","year":"2019","intvolume":"        29","citation":{"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>.","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>.","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} }","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)."},"issue":"1","title":"Theoretical properties of quasi-stationary Monte Carlo methods","doi":"http://dx.doi.org/10.1214/18-AAP1422","date_updated":"2022-09-12T07:32:35Z","volume":29,"author":[{"full_name":"Wang, Andi Q.","last_name":"Wang","first_name":"Andi Q."},{"last_name":"Kolb","id":"48880","full_name":"Kolb, Martin","first_name":"Martin"},{"full_name":"Roberts, Gareth O.","last_name":"Roberts","first_name":"Gareth O."},{"full_name":"Steinsaltz, David","last_name":"Steinsaltz","first_name":"David"}],"date_created":"2022-09-12T07:24:52Z"},{"publication":"Journal of Theoretical Probability","type":"journal_article","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."}],"status":"public","_id":"33335","department":[{"_id":"96"}],"user_id":"85821","language":[{"iso":"eng"}],"publication_status":"published","year":"2018","intvolume":"        33","page":"65–102","citation":{"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>","short":"G. Hinrichs, M. Kolb, V. Wachtel, Journal of Theoretical Probability 33 (2018) 65–102.","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} }","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>.","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>.","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>"},"publisher":"Springer Science + Business Media","date_updated":"2022-09-12T07:52:44Z","volume":33,"date_created":"2022-09-12T07:50:38Z","author":[{"last_name":"Hinrichs","full_name":"Hinrichs, Günter","first_name":"Günter"},{"first_name":"Martin","id":"48880","full_name":"Kolb, Martin","last_name":"Kolb"},{"last_name":"Wachtel","full_name":"Wachtel, Vitali","first_name":"Vitali"}],"title":"Persistence of one-dimensional AR(1)-processes","doi":"https://link.springer.com/article/10.1007/s10959-018-0850-0"},{"title":"On the dipole approximation with error estimates","doi":"https://link.springer.com/article/10.1007/s11005-017-0999-y","date_updated":"2022-09-12T08:08:09Z","date_created":"2022-09-12T08:08:05Z","author":[{"full_name":"Boßmann, Lea","last_name":"Boßmann","first_name":"Lea"},{"first_name":"Robert","last_name":"Grummt","full_name":"Grummt, Robert"},{"first_name":"Martin","last_name":"Kolb","full_name":"Kolb, Martin","id":"48880"}],"volume":108,"year":"2017","citation":{"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} }","short":"L. Boßmann, R. Grummt, M. Kolb, Letters in Mathematical Physics 108 (2017) 185–193.","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>.","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>","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>.","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>"},"page":"185–193","intvolume":"       108","publication_status":"published","language":[{"iso":"eng"}],"_id":"33336","user_id":"85821","department":[{"_id":"96"}],"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"}],"status":"public","type":"journal_article","publication":"Letters in Mathematical Physics"},{"volume":22,"date_created":"2022-09-13T07:47:39Z","author":[{"last_name":"Savov","full_name":"Savov, Mladen","first_name":"Mladen"},{"first_name":"Martin","last_name":"Kolb","id":"48880","full_name":"Kolb, Martin"}],"publisher":" Institute of Mathematical Statistics & Bernoulli Society","date_updated":"2022-09-13T07:47:46Z","doi":"https://doi.org/10.1214/17-EJP4468","title":"Conditional survival distributions of Brownian trajectories in a one dimensional Poissonian environment in the critical case","publication_status":"published","intvolume":"        22","citation":{"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>.","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>","short":"M. Savov, M. Kolb, Electronic Journal of Probability 22 (2017).","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>.","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} }","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>"},"year":"2017","department":[{"_id":"96"}],"user_id":"85821","_id":"33342","language":[{"iso":"eng"}],"publication":"Electronic Journal of Probability","type":"journal_article","status":"public","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]."}]},{"status":"public","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."}],"type":"journal_article","publication":"Mathematische Zeitschrift","language":[{"iso":"eng"}],"user_id":"85821","department":[{"_id":"96"}],"_id":"33343","citation":{"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} }","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.","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>","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>","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>.","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>."},"intvolume":"       284","page":"877-900","year":"2016","publication_status":"published","doi":"https://link.springer.com/content/pdf/10.1007/s00209-016-1677-y.pdf","title":"Spectral analysis of the diffusion operator with random jumps from the boundary","author":[{"full_name":"Kolb, Martin","id":"48880","last_name":"Kolb","first_name":"Martin"},{"first_name":"David","full_name":"Krejčiřík, David","last_name":"Krejčiřík"}],"date_created":"2022-09-13T07:56:56Z","volume":284,"date_updated":"2022-09-13T07:56:59Z","publisher":"Springer"},{"year":"2016","intvolume":"        44","citation":{"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>.","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>.","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>","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>.","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} }","short":"M. Kolb, M. Savov, The Annals of Probability 44 (2016)."},"publication_status":"published","issue":"6","title":"Transience and recurrence of a Brownian path with limited local time","doi":"http://dx.doi.org/10.1214/15-AOP1069","date_updated":"2022-09-14T04:22:26Z","publisher":"Institute of Mathematical Statistics","volume":44,"author":[{"first_name":"Martin","id":"48880","full_name":"Kolb, Martin","last_name":"Kolb"},{"first_name":"Mladen","full_name":"Savov, Mladen","last_name":"Savov"}],"date_created":"2022-09-14T04:22:23Z","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. "}],"status":"public","publication":"The Annals of Probability","type":"journal_article","language":[{"iso":"eng"}],"_id":"33357","department":[{"_id":"96"}],"user_id":"85821"},{"publisher":"INFORMS","date_updated":"2022-09-14T04:52:19Z","author":[{"first_name":"Martin","last_name":"Kolb","id":"48880","full_name":"Kolb, Martin"},{"last_name":"Stadje","full_name":"Stadje, Wolfgang","first_name":"Wolfgang"},{"first_name":"Achim","last_name":"Wübker","full_name":"Wübker, Achim"}],"date_created":"2022-09-14T04:52:15Z","volume":32,"title":"The rate of convergence to stationarity for M/G/1 models with admission controls via coupling","doi":"http://dx.doi.org/10.1080/15326349.2015.1090322","publication_status":"published","issue":"1","year":"2015","citation":{"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} }","short":"M. Kolb, W. Stadje, A. Wübker, Stochastic Models 32 (2015) 121–135.","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>.","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>","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>","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>.","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>."},"page":"121-135","intvolume":"        32","_id":"33358","user_id":"85821","department":[{"_id":"96"}],"language":[{"iso":"eng"}],"type":"journal_article","publication":"Stochastic Models","abstract":[{"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.","lang":"eng"}],"status":"public"},{"publication_status":"published","issue":"2","year":"2015","citation":{"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} }","short":"M. Kolb, D. Denisov, V. Wachtel, Journal of the London Mathematical Society 91 (2015) 495–513.","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.","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.","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."},"page":"495-513","intvolume":"        91","publisher":"London Mathematical Society","date_updated":"2022-09-14T05:01:45Z","author":[{"id":"48880","full_name":"Kolb, Martin","last_name":"Kolb","first_name":"Martin"},{"first_name":"Denis","full_name":"Denisov, Denis","last_name":"Denisov"},{"last_name":"Wachtel","full_name":"Wachtel, Vitali","first_name":"Vitali"}],"date_created":"2022-09-14T05:01:41Z","volume":91,"title":"Local asymptotics for the area of random walk excursions","type":"journal_article","publication":"Journal of the London Mathematical Society","abstract":[{"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.","lang":"eng"}],"status":"public","_id":"33360","user_id":"85821","department":[{"_id":"96"}],"language":[{"iso":"eng"}]},{"doi":"http://dx.doi.org/10.1214/ECP.v19-3006","title":"Exponential ergodicity of killed Lévy processes in a finite interval","author":[{"first_name":"Martin","full_name":"Kolb, Martin","id":"48880","last_name":"Kolb"},{"first_name":"Mladen","full_name":"Savov, Mladen","last_name":"Savov"}],"date_created":"2022-09-14T05:15:00Z","volume":19,"date_updated":"2022-09-14T05:15:06Z","publisher":"Institute of Mathematical Statistics (IMS)","citation":{"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>.","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} }","short":"M. Kolb, M. Savov, Electronic Communications in Probability 19 (2014) 1–9.","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>."},"intvolume":"        19","page":"1-9","year":"2014","issue":"31","publication_status":"published","language":[{"iso":"eng"}],"user_id":"85821","department":[{"_id":"96"}],"_id":"33361","status":"public","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.<br />","lang":"eng"}],"type":"journal_article","publication":"Electronic Communications in Probability"},{"title":"The Brownian traveller on manifolds","doi":"https://doi.org/10.4171/jst/69","date_updated":"2022-09-14T05:18:42Z","publisher":"EMS Press","date_created":"2022-09-14T05:18:39Z","author":[{"full_name":"Kolb, Martin","id":"48880","last_name":"Kolb","first_name":"Martin"},{"full_name":"Krejčiřík, David","last_name":"Krejčiřík","first_name":"David"}],"volume":4,"year":"2014","citation":{"ieee":"M. Kolb and D. Krejčiřík, “The Brownian traveller on manifolds,” <i>Journal of Spectral Theory</i>, vol. 4, no. 2, pp. 235–281, 2014, doi: <a href=\"https://doi.org/10.4171/jst/69\">https://doi.org/10.4171/jst/69</a>.","chicago":"Kolb, Martin, and David Krejčiřík. “The Brownian Traveller on Manifolds.” <i>Journal of Spectral Theory</i> 4, no. 2 (2014): 235–81. <a href=\"https://doi.org/10.4171/jst/69\">https://doi.org/10.4171/jst/69</a>.","ama":"Kolb M, Krejčiřík D. The Brownian traveller on manifolds. <i>Journal of Spectral Theory</i>. 2014;4(2):235-281. doi:<a href=\"https://doi.org/10.4171/jst/69\">https://doi.org/10.4171/jst/69</a>","apa":"Kolb, M., &#38; Krejčiřík, D. (2014). The Brownian traveller on manifolds. <i>Journal of Spectral Theory</i>, <i>4</i>(2), 235–281. <a href=\"https://doi.org/10.4171/jst/69\">https://doi.org/10.4171/jst/69</a>","mla":"Kolb, Martin, and David Krejčiřík. “The Brownian Traveller on Manifolds.” <i>Journal of Spectral Theory</i>, vol. 4, no. 2, EMS Press, 2014, pp. 235–81, doi:<a href=\"https://doi.org/10.4171/jst/69\">https://doi.org/10.4171/jst/69</a>.","short":"M. Kolb, D. Krejčiřík, Journal of Spectral Theory 4 (2014) 235–281.","bibtex":"@article{Kolb_Krejčiřík_2014, title={The Brownian traveller on manifolds}, volume={4}, DOI={<a href=\"https://doi.org/10.4171/jst/69\">https://doi.org/10.4171/jst/69</a>}, number={2}, journal={Journal of Spectral Theory}, publisher={EMS Press}, author={Kolb, Martin and Krejčiřík, David}, year={2014}, pages={235–281} }"},"page":"235-281","intvolume":"         4","publication_status":"published","issue":"2","language":[{"iso":"eng"}],"_id":"33362","user_id":"85821","department":[{"_id":"96"}],"abstract":[{"lang":"eng","text":"We study the influence of the intrinsic curvature on the large time behaviour of the heat equation in a tubular neighbourhood of an unbounded geodesic in a two-dimensional Riemannian manifold. Since we consider killing boundary conditions, there is always an exponential-type decay for the heat semigroup. We show that this exponential-type decay is slower for positively curved manifolds comparing to the flat case. As the main result, we establish a sharp extra polynomial-type decay for the heat semigroup on negatively curved manifolds comparing to the flat case. The proof employs the existence of Hardy-type inequalities for the Dirichlet Laplacian in the tubular neighbourhoods on negatively curved manifolds and the method of self-similar variables and weighted Sobolev spaces for the heat equation."}],"status":"public","type":"journal_article","publication":"Journal of Spectral Theory"},{"language":[{"iso":"eng"}],"_id":"37503","department":[{"_id":"96"}],"user_id":"85821","abstract":[{"lang":"eng","text":"This paper extends and clarifies results of Steinsaltz and Evans [Trans. Amer. Math. Soc. 359 (2007) 1285–1234], which found conditions for convergence of a killed one-dimensional diffusion conditioned on survival, to a quasistationary distribution whose density is given by the principal eigenfunction of the generator. Under the assumption that the limit of the killing at infinity differs from the principal eigenvalue we prove that convergence to quasistationarity occurs if and only if the principal eigenfunction is integrable. When the killing at ∞ is larger than the principal eigenvalue, then the eigenfunction is always integrable. When the killing at ∞ is smaller, the eigenfunction is integrable only when the unkilled process is recurrent; otherwise, the process conditioned on survival converges to 0 density on any bounded interval. "}],"status":"public","publication":"Annals of Probability","type":"journal_article","title":"Quasilimiting behavior for one-dimensional diffusions with killing","doi":"https://doi.org/10.1214/10-AOP623","publisher":"Institute of Mathematical Statistics","date_updated":"2023-01-19T06:55:09Z","volume":40,"author":[{"first_name":"Martin","last_name":"Kolb","full_name":"Kolb, Martin","id":"48880"},{"first_name":"David","last_name":"Steinsaltz","full_name":"Steinsaltz, David"}],"date_created":"2023-01-19T06:55:03Z","year":"2012","intvolume":"        40","page":"162-212","citation":{"apa":"Kolb, M., &#38; Steinsaltz, D. (2012). Quasilimiting behavior for one-dimensional diffusions with killing. <i>Annals of Probability</i>, <i>40</i>(1), 162–212. <a href=\"https://doi.org/10.1214/10-AOP623\">https://doi.org/10.1214/10-AOP623</a>","mla":"Kolb, Martin, and David Steinsaltz. “Quasilimiting Behavior for One-Dimensional Diffusions with Killing.” <i>Annals of Probability</i>, vol. 40, no. 1, Institute of Mathematical Statistics, 2012, pp. 162–212, doi:<a href=\"https://doi.org/10.1214/10-AOP623\">https://doi.org/10.1214/10-AOP623</a>.","bibtex":"@article{Kolb_Steinsaltz_2012, title={Quasilimiting behavior for one-dimensional diffusions with killing}, volume={40}, DOI={<a href=\"https://doi.org/10.1214/10-AOP623\">https://doi.org/10.1214/10-AOP623</a>}, number={1}, journal={Annals of Probability}, publisher={Institute of Mathematical Statistics}, author={Kolb, Martin and Steinsaltz, David}, year={2012}, pages={162–212} }","short":"M. Kolb, D. Steinsaltz, Annals of Probability 40 (2012) 162–212.","ama":"Kolb M, Steinsaltz D. Quasilimiting behavior for one-dimensional diffusions with killing. <i>Annals of Probability</i>. 2012;40(1):162-212. doi:<a href=\"https://doi.org/10.1214/10-AOP623\">https://doi.org/10.1214/10-AOP623</a>","chicago":"Kolb, Martin, and David Steinsaltz. “Quasilimiting Behavior for One-Dimensional Diffusions with Killing.” <i>Annals of Probability</i> 40, no. 1 (2012): 162–212. <a href=\"https://doi.org/10.1214/10-AOP623\">https://doi.org/10.1214/10-AOP623</a>.","ieee":"M. Kolb and D. Steinsaltz, “Quasilimiting behavior for one-dimensional diffusions with killing,” <i>Annals of Probability</i>, vol. 40, no. 1, pp. 162–212, 2012, doi: <a href=\"https://doi.org/10.1214/10-AOP623\">https://doi.org/10.1214/10-AOP623</a>."},"publication_status":"published","issue":"1"}]