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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RR-1171, INRIA. 1990
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  • HAL Id : inria-00075387, version 1



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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