Augmented truncation approximations of discrete-time Markov chains |
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Authors: | Yuanyuan Liu |
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Affiliation: | School of Mathematics, Railway Campus, Central South University, Changsha, Hunan 410075, China |
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Abstract: | Let P be a positive recurrent infinite transition matrix with invariant distribution π and be a truncated and arbitrarily augmented stochastic matrix with invariant distribution (n)π. We investigate the convergence ‖(n)π−π‖→0, as n→∞, and derive a widely applicable sufficient criterion. Moreover, computable bounds on the error ‖(n)π−π‖ are obtained for polynomially and geometrically ergodic chains. The bounds become rather explicit when the chains are stochastically monotone. |
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Keywords: | Truncation Markov chains Polynomial ergodicity Geometric ergodicity Queues |
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