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Klüppelberg, Claudia and Pergamenchtchikov, S. (2001): Renewal Theory for Functionals of a Markov Chain with Compact State Space. Collaborative Research Center 386, Discussion Paper 264
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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. We simplify and modify Kesten's proof.