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

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
Publication identifier
10.1016/j.spa.2021.02.001
Metadata
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Author(s)
Corujo, Josué cc
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

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