Short Communications Moderate Large Deviations Principles for Trajectories of Compound Renewal Processes

DOI10.1137/S0040585X97T989519zbMath1479.60055OpenAlexW2964379842WikidataQ127393474 ScholiaQ127393474MaRDI QIDQ5232093

Aleksandr A. Borovkov

Publication date: 29 August 2019

Published in: Theory of Probability & Its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/s0040585x97t989519

zbMATH Keywords

Cramér conditioncompound renewal processescrude (logarithmic) invariance principlemoderate large deviations principle

Mathematics Subject Classification ID

Large deviations (60F10) Functional limit theorems; invariance principles (60F17) Renewal theory (60K05)

Related Items (3)

Extension of the Invariance Principle for Compound Renewal Processes to the Zones of Moderately Large and Small Deviations ⋮ Large deviation principles for the processes admitting embedded compound renewal processes ⋮ Large deviation principles for the finite-dimensional distributions of compound renewal processes

Cites Work

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• Invariance principles for renewal processes when only moments of low order exist
• Estimate from below for large deviation probabilities of a sum of independent random variables with finite variances
• Asymptotic Analysis of Random Walks
• Stopped Random Walks
• A large deviation local limit theorem
• Cramer Large Deviations when the Extreme Conjugate Distribution is Heavy-tailed

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