New perturbation bounds for denumerable Markov chains |
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Authors: | Zahir Mouhoubi Djamil Aïssani |
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Institution: | Laboratory of Modelization and Optimization of Systems (LAMOS), Faculty of Sciences and Engineer Sciences, University of Bejaïa, 06000, Algeria |
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Abstract: | 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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Keywords: | 60J05 15A51 60J10 65F35 65F20 |
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