By A. A. Borovkov

This e-book specializes in the asymptotic habit of the possibilities of enormous deviations of the trajectories of random walks with 'heavy-tailed' (in specific, usually various, sub- and semiexponential) bounce distributions. huge deviation chances are of significant curiosity in several utilized parts, standard examples being destroy percentages in possibility thought, mistakes percentages in mathematical data, and buffer-overflow possibilities in queueing thought. The classical huge deviation thought, built for distributions decaying exponentially quickly (or even speedier) at infinity, quite often makes use of analytical tools. If the quick decay fails, that is the case in lots of vital utilized difficulties, then direct probabilistic tools often turn out to be effective. This monograph provides a unified and systematic exposition of the big deviation thought for heavy-tailed random walks. lots of the effects offered within the publication are showing in a monograph for the 1st time. lots of them have been bought by means of the authors.

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