Perturbed Markov Chains

Eilon Solan and Nicolas Vieille

We study irreducible time-homogenous Markov chains with finite state space in discrete time. We obtain results on the sensitivity of the stationary distribution and other statistical quantities with respect to perturbations of the transition matrix. We define a new closeness relation between transition matrices, and use graph-theoretic techniques, in contrast with the matrix analysis techniques previously used

This result is used in the paper “Approximating a Sequence of Observations by a Simple Process”.