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

Vadim Shcherbakov; Anatoli Yambartsev

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

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Abstract

In this note we consider a Markov chain formed by a finite system of truncated birth-death processes with local interaction. We study an asymptotic behaviour of the Markov chain as the range of possible values of its components becomes large. In particular, we show that appropriately scaled Markov chain converges to a diffusion process, and derive conditions for existence of the stationary distribution of the limit diffusion process in some special cases.

Original language	English
Journal	ArXiv.org
Publication status	Unpublished - 2016

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http://arxiv.org/abs/1606.09061

Cite this

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title = "A note on scaling limits for truncated birth-and-death processes with interaction",

abstract = "In this note we consider a Markov chain formed by a finite system of truncated birth-death processes with local interaction. We study an asymptotic behaviour of the Markov chain as the range of possible values of its components becomes large. In particular, we show that appropriately scaled Markov chain converges to a diffusion process, and derive conditions for existence of the stationary distribution of the limit diffusion process in some special cases.",

author = "Vadim Shcherbakov and Anatoli Yambartsev",

year = "2016",

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T1 - A note on scaling limits for truncated birth-and-death processes with interaction

AU - Shcherbakov, Vadim

AU - Yambartsev, Anatoli

PY - 2016

Y1 - 2016

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AB - In this note we consider a Markov chain formed by a finite system of truncated birth-death processes with local interaction. We study an asymptotic behaviour of the Markov chain as the range of possible values of its components becomes large. In particular, we show that appropriately scaled Markov chain converges to a diffusion process, and derive conditions for existence of the stationary distribution of the limit diffusion process in some special cases.

M3 - Article

JO - ArXiv.org

JF - ArXiv.org

ER -