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  3. Compound Renewal Processes
  • Cited by 1
Publisher:
Cambridge University Press
Online publication date:
June 2022
Print publication year:
2022
Online ISBN:
9781009093965
DOI:
https://doi.org/10.1017/9781009093965
Subjects:
Mathematics (general), Communications and Signal Processing, Engineering, Probability Theory and Stochastic Processes, Statistics and Probability
Series:
Encyclopedia of Mathematics and its Applications (184)
Information

Book description

Compound renewal processes (CRPs) are among the most ubiquitous models arising in applications of probability. At the same time, they are a natural generalization of random walks, the most well-studied classical objects in probability theory. This monograph, written for researchers and graduate students, presents the general asymptotic theory and generalizes many well-known results concerning random walks. The book contains the key limit theorems for CRPs, functional limit theorems, integro-local limit theorems, large and moderately large deviation principles for CRPs in the state space and in the space of trajectories, including large deviation principles in boundary crossing problems for CRPs, with an explicit form of the rate functionals, and an extension of the invariance principle for CRPs to the domain of moderately large and small deviations. Applications establish the key limit laws for Markov additive processes, including limit theorems in the domains of normal and large deviations.

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