## Electronic Communications in Probability

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

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

#### 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