Perturbed Markov chains

Nicolas Vieille (1) , Eilon Solan (2)

1 GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC
2 TAU - Tel Aviv University

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.

Keywords: Markov chains; stationary distribution; exit distribution; conductance; sensitivity analysis; perturbation theory; stability of a Markov chain

Domains: Economy and decision science

Nicolas Vieille, Eilon Solan. Perturbed Markov chains. Journal of Applied Probability, 2003, Vol.40,n°1, pp.107-122. ⟨10.1239/jap/1044476830⟩. ⟨hal-00464967⟩