Extension of the Invariance Principle for Compound Renewal Processes to the Zones of Moderately Large and Small Deviations

DOI10.1137/S0040585X97T990095zbMath1455.60118OpenAlexW3129127966MaRDI QIDQ5150153

Aleksandr A. Borovkov

Publication date: 9 February 2021

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

Full work available at URL: https://doi.org/10.1137/s0040585x97t990095

zbMATH Keywords

invariance principlelarge deviationsrandom walkcompound renewal processsmall deviations

Mathematics Subject Classification ID

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

Cites Work

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• Large deviation principles in boundary problems for compound renewal processes
• Fourier method for determining the asymptotic behavior of small deviations of a Wiener process
• Invariance principles for renewal processes
• On the optimality of strong approximation rates for compound renewal processes
• Invariance principles for renewal processes when only moments of low order exist
• Probability theory. Edited by K. A. Borovkov. Transl. from the Russian by O. Borovkova and P. S. Ruzankin
• Functional limit theorems for compound renewal processes
• Distribution of the maximum of a process with independent increments
• An approximation of stopped sums with applications in queueing theory
• An approximation of partial sums of independent RV's, and the sample DF. II
• An approximation of partial sums of independent RV'-s, and the sample DF. I
• Small Deviations in a Space of Trajectories
• Short Communications Moderate Large Deviations Principles for Trajectories of Compound Renewal Processes

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