Dynamics of a Fleming-Viot type particle system on the cycle graph

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:136

Article

Corujo, Josue^1,2 

[1] PSL Univ, Univ Paris Dauphine, CEREMADE, Pl Marechal Lattre Tassigny, F-75016 Paris, France

[2] Univ Toulouse, Inst Math Toulouse, Inst Natl Sci Appl Toulouse, 135 Ave Rangueil, F-31400 Toulouse, France

关键词: Quasi-stationary distribution;    Fleming-Viot type particle system;    Moran type model;    Propagation of chaos;    Ergodicity;   

DOI  :  10.1016/j.spa.2021.02.001

来源: Elsevier

【 摘 要 】

We study the Fleming-Viot particle process formed by N interacting continuous-time asymmetric random walks on the cycle graph, with uniform killing. We show that this model has a remarkable exact solvability, despite the fact that it is non-reversible with non-explicit invariant distribution. Our main results include quantitative propagation of chaos and exponential ergodicity with explicit constants, as well as formulas for covariances at equilibrium in terms of the Chebyshev polynomials. We also obtain a bound uniform in time for the convergence of the proportion of particles in each state when the number of particles goes to infinity. (C) 2021 Elsevier B.V. All rights reserved.

【 授权许可】

Free