Asymptotic Analysis of Random Walks

Light-Tailed Distributions

A. A. Borovkov, V. V. Ulyanov, Mikhail Zhitlukhin

• Publisher: Cambridge University Press
• Year: 2020
• ISBN:
  9781108907798
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

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.

Table of contents

• Cover
• Half-title
• Series information
• Title page
• Copyright information
• Contents
• Introduction
• 1 Preliminary results
• 2 Approximation of distributions of sums of random variables
• 3 Boundary crossing problems for random walks
• 4 Large deviation principles for random walk trajectories
• 5 Moderately large deviation principles for the trajectories of random walks and processes with independent increments
• 6 Some applications to problems in mathematical statistics
• Basic notation
• References
• Index