The Annals of Probability

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

Claudia Klüppelberg and Serguei Pergamenchtchikov

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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.

Article information

Ann. Probab., Volume 31, Number 4 (2003), 2270-2300.

First available in Project Euclid: 12 November 2003

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Zentralblatt MATH identifier

Primary: 60J05: Discrete-time Markov processes on general state spaces 60K05: Renewal theory 60K15: Markov renewal processes, semi-Markov processes 60H25: Random operators and equations [See also 47B80]

Key Renewal Theorem Markov chain random recurrence equation Riemann integrability


Klüppelberg, Claudia; Pergamenchtchikov, Serguei. Renewal theory for functionals of a Markov chain with compact state space. Ann. Probab. 31 (2003), no. 4, 2270--2300. doi:10.1214/aop/1068646385.

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