Sur l'approximation de la distribution stationnaire d'une chaîne de Markov stochastiquement monotone

F. Simonot

Stochastic Processes and their Applications, 1995, vol. 56, issue 1, 133-149

Abstract: Let P be an infinite irreducible stochastic matrix, stochastically dominated by an irreducible, positive-recurrent and stochastically monotone stochastic matrix Q. Let Pn be any n x n stochastic matrix with Pn [greater-or-equal, slanted] Tn, where Tn denotes the n x n northwest corner truncation of P. We first show that these assumptions imply the existence of limiting distributions [mu], [pi], [pi]n for Q, P, Pn respectively; moreover, if Q obeys a Foster-Lyapounov condition, we derive the rate of convergence of [pi]n to [pi]; as an application of the preceding results, we deal with the random walk on a half line, and prove under mild assumptions that the rate of convergence of [pi]n to [pi] is geometric.

Keywords: Markov; chains; Augmented; truncation; Approximation; Limit; distribution; Stochastically; monotone; Random; walk (search for similar items in EconPapers)
Date: 1995
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