We derive necessary and sufficient conditions for the existence of bounded or summable solutions to systems of linear equations associated with Markov chains. This substantially extends a famous ...

Markov Models for disease progression are common in medical decision making (see references below). The parameters in a Markov model can be estimated by observing the time it takes patients in any ...

This paper is the discrete time counterpart of the previous work in the continuous time case by Guillin, Léonard, the second named author and Yao [Probab. Theory Related Fields 144 (2009), 669–695].

A Markov chain is a sequence of random variables that satisfies P(X t+1 ∣X t ,X t−1 ,…,X 1 )=P(X t+1 ∣X t ). Simply put, it is a sequence in which X t+1 depends only on X t and appears before X t−1 ...