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

2012/07/05 by Boris Tsirelson, Tsirelson, Boris
Computer Science · Decision Sciences · Mathematics · #Bayesian Modeling and Causal Inference #Decision-Making and Behavioral Economics #FOS: Mathematics #Game Theory and Applications #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.1207.1290

16 pages

arxiv created 2012/07/05 · openalex publication_date 2012/07/05 · arxiv updated 2012/07/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

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• Quenched large deviations in renewal theory
• Large Deviations in Renewal Theory and Renewal Models of Statistical Mechanics
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• Large deviations for renewal processes
• Limit Forms of the Distribution of the Number of Renewals