By A. A. Borovkov

ISBN-10: 0511721390

ISBN-13: 9780511721397

ISBN-10: 052188117X

ISBN-13: 9780521881173

This e-book specializes in the asymptotic habit of the possibilities of huge deviations of the trajectories of random walks with 'heavy-tailed' (in specific, on a regular basis various, sub- and semiexponential) leap distributions. huge deviation chances are of significant curiosity in different utilized parts, standard examples being destroy percentages in hazard conception, errors percentages in mathematical records, and buffer-overflow possibilities in queueing concept. The classical huge deviation thought, constructed for distributions decaying exponentially speedy (or even quicker) at infinity, in general makes use of analytical equipment. If the short decay fails, that's the case in lots of vital utilized difficulties, then direct probabilistic tools often end up to be effective. This monograph offers a unified and systematic exposition of the massive deviation conception for heavy-tailed random walks. lots of the effects offered within the booklet are showing in a monograph for the 1st time. a lot of them have been acquired by means of the authors.