A note on scaling limits for truncated birth-and-death processes with interaction

2016/06/29 by Vadim Shcherbakov, Anatoly Yambartsev, Shcherbakov, Vadim +1
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Diffusion and Search Dynamics #FOS: Mathematics #Opinion Dynamics and Social Influence #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1606.09061

openalex publication_date 2016/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we consider a Markov chain formed by a finite system of interacting birth-and-death processes on a finite state space. We study an asymptotic behaviour of the Markov chain as its state space becomes large. In particular, we show that the appropriately scaled Markov chain converges to a diffusion process, and derive conditions for existence of the stationary distribution of the limit diffusion process in special cases.

Citations

• Birth and Death process in mean field type interaction

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