Asymptotic Analysis of Multiscale Markov Chain

2015/12/30 by Wei Zhang, Zhang, Wei
Mathematics · #34E05 #34E13 #60J27 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:34E05 #msc:34E13 #msc:60J27

paper · pdf · doi:10.48550/arxiv.1512.08944

25 pages

arxiv created 2016/01/27 · arxiv updated 2016/01/28

Abstract

We consider continuous-time Markov chain on a finite state space X. We assume X can be clustered into several subsets such that the intra-transition rates within these subsets are of order O(\frac1ε) comparing to the inter-transition rates among them, where 0 < ε≪ 1. Several asymptotic results are obtained as ε→ 0 concerning the convergence of Kolmogorov backward equation, Poincaré constant, (modified) logarithmic Sobolev constant to their counterparts of certain reduced Markov chain. Both reversible and irreversible Markov chains are considered.

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