A Computational Framework for the Mixing Times in the QBD Processes with Infinitely-Many Levels

2013/08/20 by Li, Quan-Lin, Cao, Jing
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paper · doi:10.48550/arxiv.1308.4227

Abstract

In this paper, we develop some matrix Poisson's equations satisfied by the mean and variance of the mixing time in an irreducible positive-recurrent discrete-time Markov chain with infinitely-many levels, and provide a computational framework for the solution to the matrix Poisson's equations by means of the UL-type of RG-factorization as well as the generalized inverses. In an important special case: the level-dependent QBD processes, we provide a detailed computation for the mean and variance of the mixing time. Based on this, we give new highlight on computation of the mixing time in the block-structured Markov chains with infinitely-many levels through the matrix-analytic method.

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