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Transient phenomena for Markov chains and their applications

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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Submitted on : Wednesday, May 24, 2006 - 6:07:08 PM
Last modification on : Friday, February 4, 2022 - 3:18:43 AM
Long-term archiving on: : Tuesday, April 12, 2011 - 6:47:27 PM

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  • HAL Id : inria-00075387, version 1

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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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