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5 - Integro-Local Limit Theorems under the Cramér Moment Condition

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 integro-local probabilities that was initiated in Chapter 2 in the normal deviation zone. Now, assuming that the vector (?, ?) satisfies the Cramér moment condition, we study the integro-local probability in a wider zone, which in analogy with random walks can be called the Cramér deviation zone. This zone includes the zones of normal, moderately large, and "usual" large deviations.

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Chapter
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Compound Renewal Processes , pp. 225 - 274
Publisher: Cambridge University Press
Print publication year: 2022

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