Asymptotic Analysis of Random Walks: Light-Tailed Distributions (Encyclopedia of Mathematics and its Applications, Series Number 176)

This is a companion book to Asymptotic Analysis of Random Walks: Heavy-Tailed Distributions by A.A. Borovkov and K.A. Borovkov. Its self-contained systematic exposition provides a highly useful resource for academic researchers and professionals interested in applications of probability in statistics, ruin theory, and queuing theory. The large deviation principle for random walks was first established by the author in 1967, under the restrictive condition that the distribution tails decay faster than exponentially. (A close assertion was proved by S.R.S. Varadhan in 1966, but only in a rather special case.) Since then, the principle has always been treated in the literature only under this condition. Recently, the author jointly with A.A. Mogul'skii removed this restriction, finding a natural metric for which the large deviation principle for random walks holds without any conditions. This new version is presented in the book, as well as a new approach to studying large deviations in boundary crossing problems. Many results presented in the book, obtained by the author himself or jointly with co-authors, are appearing in a monograph for the first time.

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).