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OverviewCompound 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. Full Product DetailsAuthor: A. A. Borovkov , Alexey Alimov (Steklov Institute of Mathematics, Moscow)Publisher: Cambridge University Press Imprint: Cambridge University Press Dimensions: Width: 16.50cm , Height: 2.10cm , Length: 24.10cm Weight: 0.700kg ISBN: 9781009098441ISBN 10: 1009098446 Pages: 379 Publication Date: 30 June 2022 Audience: College/higher education , Tertiary & Higher Education Format: Hardback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of ContentsIntroduction; 1. Main limit laws in the normal deviation zone; 2. Integro-local limit theorems in the normal deviation zone; 3. Large deviation principles for compound renewal processes; 4. Large deviation principles for trajectories of compound renewal processes; 5. Integro-local limit theorems under the Cramér moment condition; 6. Exact asymptotics in boundary crossing problems for compound renewal processes; 7. Extension of the invariance principle to the zones of moderately large and small deviations; A. On boundary crossing problems for compound renewal processes when the Cramér condition is not fulfilled; Basic notation; References; Index.ReviewsAuthor InformationA. 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. Tab Content 6Author Website:Countries AvailableAll regions |
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