Birth and Death process in mean field type interaction
Abstract
The aim of this paper is to study the asymptotic behavior of a system of birth and death processes in mean field type interaction in discrete space. We first establish the exponential convergence of the particle system to equilibrium for a suitable Wasserstein coupling distance. The approach provides an explicit quantitative estimate on the rate of convergence. We prove next a uniform propagation of chaos property. As a consequence, we show that the limit of the associated empirical distribution, which is the solution of a nonlinear differential equation, converges exponentially fast to equilibrium. This paper can be seen as a discrete version of the particle approximation of the McKean-Vlasov equations and is inspired from previous works of Malrieu and al and Caputo, Dai Pra and Posta.
Cite
@article{arxiv.1510.03238,
title = {Birth and Death process in mean field type interaction},
author = {Marie-Noémie Thai},
journal= {arXiv preprint arXiv:1510.03238},
year = {2015}
}