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”.