A note on scaling limits for truncated birth-and-death processes with interaction
Probability
2016-11-14 v2
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.
Cite
@article{arxiv.1606.09061,
title = {A note on scaling limits for truncated birth-and-death processes with interaction},
author = {Vadim Shcherbakov and Anatoly Yambartsev},
journal= {arXiv preprint arXiv:1606.09061},
year = {2016}
}