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New perturbation bounds for denumerable Markov chains

✍ Scribed by Zahir Mouhoubi; Djamil Aïssani

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
305 KB
Volume
432
Category
Article
ISSN
0024-3795

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✦ Synopsis

This paper is devoted to perturbation analysis of denumerable Markov chains. Bounds are provided for the deviation between the stationary distribution of the perturbed and nominal chain, where the bounds are given by the weighted supremum norm. In addition, bounds for the perturbed stationary probabilities are established. Furthermore, bounds on the norm of the asymptotic decomposition of the perturbed stationary distribution are provided, where the bounds are expressed in terms of the norm of the ergodicity coefficient, or the norm of a special residual matrix. Refinements of our bounds for Doeblin Markov chains are considered as well. Our results are illustrated with a number of examples.

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