Asymptotic Analysis of Random Walks - Light-Tailed Distributions

List of contents

1. Preliminaries; 2. Distribution approximations for sums of random variables; 3 Boundary problems for random walks; 4. Large deviation principles for trajectories of random walks; 5. Moderately large deviation principles for trajectories of random walks and processes with independent increments; 6. Applications to mathematical statistics.

About the author

A.A. Borovkov is Principal Research Fellow and a Russian Academy of Sciences Adviser at the Sobolev Institute of Mathematics, where he also served as the founding head of the Department of Probability Theory and Mathematical Statistics. He was the founding Chair in Probability Theory and Mathematical Statistics at the Novosibirsk State University in 1965. He has authored and co-authored several influential research monographs. In 1979 he was awarded (together with V.V. Sazonov and V. Statulevičius) the State Prize of the USSR for outstanding research results on asymptotic methods of probability theory, and was elected a full member of the Academy of Sciences of the USSR in 1990. He received the 2002 Russian Government Prize in Education, the 2003 Russian Academy of Sciences A.A. Markov Prize, and the Russian Academy of Sciences A.A. Kolmogorov Prize for his joint work with A.A. Mogul'skii on the extended large deviation principle (2015).

Summary

This is a complete and systematic modern treatise on large deviation theory for random walks with light-tailed jump distributions, presented by one of its key creators. Such distributions have numerous applications in statistics, ruin theory, and queuing theory. This is a companion to the author's earlier monograph on heavy-tailed distributions.

Product details

• Authors: A A Borovkov, A. a. Borovkov, A.a. (Sobolev Institute of Mathematics Borovkov, Borovkov A. A.
• Assisted by: V V Ulyanov (Translation), V. V. Ulyanov (Translation), V.V. Ulyanov (Translation), Mikhail Zhitlukhin (Translation), Mikhail (Steklov Institute of Mathematics Zhitlukhin (Translation)
• Publisher: Cambridge University Press ELT
• Languages: English
• Product format: Hardback
• Released: 29.10.2020
• EAN: 9781107074682
• ISBN: 978-1-107-07468-2
• No. of pages: 450
• Series: Encyclopedia of Mathematics and Its Applications; Encyclopedia of Mathematics an
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Miscellaneous; MATHEMATICS / Probability & Statistics / General, MATHEMATICS / Applied, Probability & statistics, Stochastics, Mathematical modelling, Probability and statistics