Birth and Death process in mean field type interaction

2015/10/12 by Marie-Noémie Thai, Thai, Marie-Noémie · 3 citations
Mathematics · Physics and Astronomy · #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.1510.03238

openalex publication_date 2015/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• An alternate Lagrangian scheme for spatially inhomogeneous evolutionary\n games
• A Large Scale Analysis of Unreliable Stochastic Networks
• A note on scaling limits for truncated birth-and-death processes with interaction

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