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

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  • Simonot, F.

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.

Suggested Citation

  • Simonot, F., 1995. "Sur l'approximation de la distribution stationnaire d'une chaîne de Markov stochastiquement monotone," Stochastic Processes and their Applications, Elsevier, vol. 56(1), pages 133-149, March.
    • Handle: RePEc:eee:spapps:v:56:y:1995:i:1:p:133-149
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    References listed on IDEAS

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    1. Gibson, Diana & Seneta, E., 1987. "Monotone infinite stochastic matrices and their augmented truncations," Stochastic Processes and their Applications, Elsevier, vol. 24(2), pages 287-292, May.
    2. Nico M. van Dijk, 1991. "Truncation of Markov Chains with Applications to Queueing," Operations Research, INFORMS, vol. 39(6), pages 1018-1026, December.
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