Abstract
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 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.
Acknowledgments
The authors thank A. Klump for useful discussions about the topic of this work.
Citation
Martin Kolb. Matthias Liesenfeld. "On non-extinction in a Fleming-Viot-type particle model with Bessel drift." Electron. J. Probab. 27 1 - 28, 2022. https://doi.org/10.1214/22-EJP866
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