An Approach to the Study of Infinite Markov Chains from the Drazin Inverse of a Core-Nilpotent Operator

Abstract

The Drazin inverse is the most important psuedo-inveserse of linear operators of finite-dimensional vector spaces. One of its applications is in fininte Markov chains theory, where they are used to calculate certain properties such as the average number of times the chain passes through a particular state or the expected time it takes for the chain to enter it. Since it has been possible to generalize Drazin's inverse to linear operators in arbitrary dimension (Core-Nilpotent Operators), the aim of this paper is to use it to obtain the same results for infinite Markov chains. Futhermore, the results will be applied to a concrete example.