Summary: SINGULARLY PERTURBED FINITE
MARKOV CHAINS WITH GENERAL
ERGODIC STRUCTURE
Konstantin E. Avrachenkov
INRIA Sophia Antipolis, 2004 Route des Lucioles,
B.P.93, 06902, Sophia Antipolis Cedex, France
k.avrachenkov@sophia.inria.fr
Keywords: Finite Markov chains, singular perturbations, asymptotic power series.
Abstract We analyse singularly perturbed Markov chains. Most previous research
has been done under the assumption that the perturbed Markov chain
is either ergodic or unichain. In this paper we do not impose any re­
strictions on the ergodic structure of the perturbed chain. The present
approach is based on the inversion of analytic matrix­valued functions.
Introduction
In this paper we consider a perturbed Markov chain with the transi­
tion probability matrix P ('') = P (0) + ''C, where P (0) 2 IR n\Thetan is the
transition matrix of the unperturbed chain and '' is a small perturbation
parameter. The aim of this paper is to calculate the asymptotic expan­
sions for the stationary distributions and the absorption probabilities of
the perturbed Markov chain. We are mostly interested in the case of sin­

Source: Avrachenkov, Konstantin - INRIA Sophia Antipolis

Collections: Computer Technologies and Information Sciences