Explicit solutions and decay rates for a general class of Markov chains

J.S.H. Leeuwaarden, van, M.S. Squillante, E.M.M. Winands

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Abstract

In this paper we consider a general class of infinite multidimensional Markov chains and derive explicit solutions for their stationary distribution and tail asymptotics. More specifically, we present an exact matrixgeometric solution for the stationary probability vector. We reformulate the probabilistic interpretations of the fundamental solution matrices in terms of Bernoulli excursions, leading to explicit expressions for these matrix elements in terms of hypergeometric functions. We establish asymptotic results on the powers of one of the fundamental solution matrices, which are used together with the corresponding matrix element expressions to obtain explicit large-deviation decay rates.
Original languageEnglish
Title of host publicationBook of Abstracts of the 14th INFORMS Applied Probability Conference, July 9-11, 2007
Place of PublicationEindhoven
PublisherEurandom & TU/e
Pages137-
Publication statusPublished - 2007
Event14th INFORMS Applied Probability Conference (APS 2007) - Eindhoven, Netherlands
Duration: 9 Jul 200711 Jul 2007

Conference

Conference14th INFORMS Applied Probability Conference (APS 2007)
CountryNetherlands
CityEindhoven
Period9/07/0711/07/07

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