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4 - Large Deviation Principles for Trajectories of Compound Renewal Processes

Published online by Cambridge University Press:  16 June 2022

A. A. Borovkov
Translated by
Alexey Alimov
A. A. Borovkov
Affiliation:
Sobolev Institute of Mathematics, Russia
Alexey Alimov
Affiliation:
Steklov Institute of Mathematics, Moscow
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Summary

We continue the study of large deviation principles for compound renewal processes. We are mostly concerned with probabilities of large deviations of the trajectories of CRPs. We establish "partial" LDPs (local LDPs applicable only in the space of absolutely continuous functions). "Complete" LDPs are obtained under rather restrictive conditions. It proves possible to obtain LDPs for boundary crossing problems under broader conditions and with explicit deviation functional. A moderately large deviation principle for CRPs is established.

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Compound Renewal Processes , pp. 154 - 224
Publisher: Cambridge University Press
Print publication year: 2022

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