Electronic Communications in Probability

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

Boris Tsirelson

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465315591

Digital Object Identifier
doi:10.1214/ECP.v18-2719

Mathematical Reviews number (MathSciNet)
MR3078015

Zentralblatt MATH identifier
1300.60039

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

Keywords
moderate deviation uniform renewal theorem renewal-reward

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

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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References

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