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Published online by Cambridge University Press: 16 June 2022
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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