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

  • Mikael PeterssonEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 179)

Abstract

In this paper we study quasi-stationary distributions of non-linearly perturbed semi-Markov processes in discrete time. This type of distributions are of interest for 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.

Keywords

Semi-Markov process Perturbation Quasi-stationary distribution Asymptotic expansion Renewal equation Markov chain 

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of MathematicsStockholm UniversityStockholmSweden

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