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Corpus ID: 119599145

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

@article{Shcherbakov2016ANO,
title={A note on scaling limits for truncated birth-and-death processes with interaction},
author={V. Shcherbakov and A. Yambartsev},
journal={arXiv: Probability},
year={2016}
}

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.