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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.
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