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Engineering Mathematics II pp 131–149Cite as

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

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((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.

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Authors and Affiliations

  1. Department of Mathematics, Stockholm University, SE-106 91, Stockholm, Sweden

    Mikael Petersson

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  1. Mikael Petersson
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Correspondence to Mikael Petersson .

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Editors and Affiliations

  1. Division of Applied Mathematics, School of Education, Culture and Communication, Mälardalen University,, Västerås, Sweden

    Sergei Silvestrov

  2. Division of Applied Mathematics,, School of Education, Culture and Communication, Mälardalen University, Västerås, Sweden

    Milica Rančić

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Petersson, M. (2016). Asymptotics for Quasi-stationary Distributions of Perturbed Discrete Time Semi-Markov Processes. In: Silvestrov, S., Rančić, M. (eds) Engineering Mathematics II. Springer Proceedings in Mathematics & Statistics, vol 179. Springer, Cham. https://doi.org/10.1007/978-3-319-42105-6_9

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