Title Asymptotic analysis of random walks : heavy-tailed distributions / A.A. Borovkov, K.A. Borovkov ; translated by O.B. Borovkova

Published Cambridge : Cambridge University Press, 2008

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Description 1 online resource (xxix, 625 pages) : illustrations Series Encyclopedia of mathematics and its applications ; number 118 Encyclopedia of mathematics and its applications ; no. 118. Contents Preliminaries -- Random walks with jumps having no finite first moment -- Random walks with jumps having finite mean and infinite variance -- Random walks with jumps having finite variance -- Random walks with semiexponential jump distributions -- Large deviations on the boundary of and outside the Cramer zone for random walks with jump distributions decaying exponentially fast -- Asymptotic properties of functions of regularly varying and semiexponential distributions. Asymptotics of the distributions of stopped sums and their maxima. An alternative approach to studying the asymptotics of P(S[subscript n] [is equal to or greater than] x) -- On the asymptotics of the first hitting times -- Integro-local and integral large deviation theorems for sums of random vectors -- Large deviations in trajectory space -- Large deviations of sums of random variables of two types -- Random walks with non-identically distributed jumps in the triangular array scheme in the case of infinite second moment. Transient phenomena -- Random walks with non-identically distributed jumps in the triangular array scheme in the case of finite variances -- Random walks with dependent jumps -- Extension of the results of Chapters 2-5 to continuous-time random processes with independent increments -- Extension of the results of Chapters 3 and 4 to generalized renewal processes Summary This monograph is devoted to studying the asymptotic behaviour of the probabilities of large deviations of the trajectories of random walks, with 'heavy-tailed' (in particular, regularly varying, sub- and semiexponential) jump distributions. It presents a unified and systematic exposition Bibliography Includes bibliographical references and index Notes Print version record Subject Random walks (Mathematics) Asymptotic expansions. MATHEMATICS -- Applied. MATHEMATICS -- Probability & Statistics -- General. Asymptotic expansions Random walks (Mathematics) Asymptotik Irrfahrtsproblem Form Electronic book Author Borovkov, K. A. (Konstantin Aleksandrovich) ISBN 9781461941576 1461941571 9780511826276 0511826273 9780511721397 0511721390 9781107390522 1107390524

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