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3 - Large Deviation Principles for 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 study the nature of the distributions of CRPs in the large deviation zone and establish the corresponding LDPs. We clarify the relation of the distribution of a CRP with the renewal measure for the sequence {Tn, Zn}. We investigate some properties of the deviation functions of the renewal measures that appear in this problem. We prove the LDPs for the CRPs Z(t). The definition of the fundamental function is given, and we also study its properties and relations to the deviation functions. We present several results on LDPs for the process Y(t) and for Markov additive processes.

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Compound Renewal Processes , pp. 90 - 153
Publisher: Cambridge University Press
Print publication year: 2022

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