Reduction of Markov chains with two-time-scale state transitions

Abstract

In this paper, we consider a general class of two-time-scale Markov chains whose transition rate matrix depends on a parameter $\lambda >0$. We assume that some transition rates of the Markov chain will tend to infinity as $\lambda \to \infty$. We divide the state space of the Markov chain $X$ into a fast state space and a slow state space and define a reduced chain $Y$ on the slow state space. Our main result is that the distribution of the original chain $X$ will converge in total variation distance to that of the reduced chain $Y$ uniformly in time $t$ as $\lambda \to \infty$.

30 pages, 3 figures; Stochastics: An International Journal of Probability and Stochastic Processes, 2015

References in corpus (1)

• Singularly perturbed Markov chains: Limit results and applications

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