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

Vadim Shcherbakov; Anatoly Yambartsev

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arXiv · 1606.09061

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

Vadim Shcherbakov·Anatoly Yambartsev

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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.

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Vadim Shcherbakov, Anatoly Yambartsev. 2016-06-29. A note on scaling limits for truncated birth-and-death processes with interaction. https://arxiv.org/abs/1606.09061

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