Compound Renewal Processes (Encyclopedia of Mathematics and its Applications, Series Number 184) - Hardcover

Borovkov, A. A.

Hardcover

ISBN 10: 1009098446 ISBN 13: 9781009098441

Publisher: Cambridge University Press, 2022

Synopsis

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.

About this title

About the Author

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.

Edition details

• Publisher: Cambridge University Press
• Publication date: 2022
• Language: English
• ISBN 10: 1009098446
• ISBN 13: 9781009098441
• Binding: Hardcover
• Edition number: 1
• Number of pages: 379