Asymptotic Analysis of Multiscale Markov Chain
Abstract
We consider continuoustime Markov chain on a finite state space X. We assume X can be clustered into several subsets such that the intratransition rates within these subsets are of order $\mathcal{O}(\frac{1}{\epsilon})$ comparing to the intertransition rates among them, where $0 < \epsilon \ll 1$. Several asymptotic results are obtained as $\epsilon \rightarrow 0$ 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.
 Publication:

arXiv eprints
 Pub Date:
 December 2015
 arXiv:
 arXiv:1512.08944
 Bibcode:
 2015arXiv151208944Z
 Keywords:

 Mathematics  Probability;
 60J27;
 34E13;
 34E05
 EPrint:
 25 pages