Asymptotics for Quasi-Stationary Distributions of Perturbed Discrete Time Semi-Markov Processes

2016/03/18 by Petersson, Mikael
#60J10 #60K05 #FOS: Mathematics #Primary 60K15 #Probability (math.PR) #Secondary 41A60

paper · doi:10.48550/arxiv.1603.05895

Abstract

In this paper, we study quasi-stationary distributions of nonlinearly perturbed semi-Markov processes in discrete time. This type of distributions is of interest for the analysis of stochastic systems which have finite lifetimes, but are expected to persist for a long time. We obtain asymptotic power series expansions for quasi-stationary distributions and it is shown how the coefficients in these expansions can be computed from a recursive algorithm. As an illustration of this algorithm, we present a numerical example for a discrete time Markov chain.

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