{"author":[{"last_name":"Kolb","id":"48880","full_name":"Kolb, Martin","first_name":"Martin"},{"full_name":"Liesenfeld, Matthias","last_name":"Liesenfeld","first_name":"Matthias"}],"publisher":"Institute of Mathematical Statistics","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","year":"2022","citation":{"bibtex":"@article{Kolb_Liesenfeld_2022, title={On non-extinction in a Fleming-Viot-type particle model with Bessel drift}, DOI={<a href=\"https://doi.org/10.1214/22-EJP866\">https://doi.org/10.1214/22-EJP866</a>}, number={27}, journal={Electronic Journal of Probability}, publisher={Institute of Mathematical Statistics}, author={Kolb, Martin and Liesenfeld, Matthias}, year={2022}, pages={1–28} }","chicago":"Kolb, Martin, and Matthias Liesenfeld. “On Non-Extinction in a Fleming-Viot-Type Particle Model with Bessel Drift.” <i>Electronic Journal of Probability</i>, no. 27 (2022): 1–28. <a href=\"https://doi.org/10.1214/22-EJP866\">https://doi.org/10.1214/22-EJP866</a>.","short":"M. Kolb, M. Liesenfeld, Electronic Journal of Probability (2022) 1–28.","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>.","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>.","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>"},"user_id":"85821","date_created":"2023-01-10T08:19:25Z","department":[{"_id":"96"}],"_id":"35649","title":"On non-extinction in a Fleming-Viot-type particle model with Bessel drift","issue":"27","publication_status":"published","language":[{"iso":"eng"}],"page":"1-28","publication":"Electronic Journal of Probability","date_updated":"2023-01-10T08:19:38Z","type":"journal_article","doi":"https://doi.org/10.1214/22-EJP866"}