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Reports Year : 1990

Transient phenomena for Markov chains and their applications

A.A. Borovkov
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Guy Fayolle
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D.A. Korshunov
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Abstract

In this paper we consider a family of irreductible, ergodic and aperiodic Markov chains, depending on a parameter e > 0, so that the local drifts have a critical behaviour (in terms of Pakes lemma). The purpose is to analyze the steady state distributions of these chains (in the sense of weak convergence), when e ¯ 0. Under assumptions involving at most the existence of moments of order 2 + g for the jumps, we show that, whenever X (0) is not ergodic, it is possible to caracterize accurately these limit distributions. Connections with the gamma and uniform distributions are revealed.

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Other [cs.OH]
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Dates and versions

inria-00075387 , version 1 (24-05-2006)

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  • HAL Id : inria-00075387 , version 1

Cite

A.A. Borovkov, Guy Fayolle, D.A. Korshunov. Transient phenomena for Markov chains and their applications. RR-1171, INRIA. 1990. ⟨inria-00075387⟩
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