Compound Renewal Processes

A. A. Borovkov, Alexey Alimov (Steklov Institute of Mathematics, Moscow)

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English

Cambridge University Press
30 June 2022

Information theory; Probability & statistics; Mathematical modelling; Stochastics

Series: Encyclopedia of Mathematics and its Applications

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.

By: A. A. Borovkov
Translated by: Alexey Alimov (Steklov Institute of Mathematics Moscow)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Dimensions: Height: 241mm, Width: 165mm, Spine: 21mm
Weight: 700g
ISBN: 9781009098441
ISBN 10: 1009098446
Series: Encyclopedia of Mathematics and its Applications
Pages: 379
Publication Date: 30 June 2022
Audience: College/higher education , Primary
Format: Hardback
Publisher's Status: Active

A. A. Borovkov has authored and co-authored about 300 peer-reviewed research papers, seven influential research monographs, and two university textbooks. He received the 1979 USSR State Prize, the Russian Academy of Sciences A. A. Markov Prize (2003), and the A. N. Kolmogorov Prize (2015) for his research in the area of probability theory.