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