Electronic Communications in Probability

From uniform renewal theorem to uniform large and moderate deviations for renewal-reward processes

Boris Tsirelson

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A uniform key renewal theorem is deduced from the uniform Blackwell's renewal theorem. A uniform LDP (large deviation principle) for renewal-reward processes is obtained, and MDP (moderate deviation principle) is deduced under conditions much weaker than existence of exponential moments.

Article information

Electron. Commun. Probab., Volume 18 (2013), paper no. 52, 13 pp.

Accepted: 27 June 2013
First available in Project Euclid: 7 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60F10: Large deviations
Secondary: 60K05: Renewal theory 60K15: Markov renewal processes, semi-Markov processes

moderate deviation uniform renewal theorem renewal-reward

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Tsirelson, Boris. From uniform renewal theorem to uniform large and moderate deviations for renewal-reward processes. Electron. Commun. Probab. 18 (2013), paper no. 52, 13 pp. doi:10.1214/ECP.v18-2719. https://projecteuclid.org/euclid.ecp/1465315591

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