Renewal theory for functionals of a markov chain with compact state space

Abstract

Motivated by multivariate random recurrence equations we prove a new analogue of the Key Renewal Theorem for functionals of a Markov chain with compact state space in the spirit of Kesten [Ann. Probab. 2 (1974) 355-386], Compactness of the state space and a certain continuity condition allows us to simplify Kesten's proof considerably.