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

Corujo, Josué

Corujo, Josué (2021), Dynamics of a Fleming–Viot type particle system on the cycle graph, Stochastic Processes and their Applications, 136, p. 57-91. 10.1016/j.spa.2021.02.001

Type

Article accepté pour publication ou publié

External document link

https://hal.archives-ouvertes.fr/hal-02447747v2

Date

2021-01

Journal name

Stochastic Processes and their Applications

Volume

136

Publisher

Elsevier

Pages

57-91

CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Institut de Mathématiques de Toulouse UMR5219 [IMT]

Abstract (EN)

We study the Fleming–Viot particle process formed by 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.

Subjects / Keywords

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