Research Catalog

Title

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

Author

Borovkov, Aleksandr Alekseevich.

Publication

Cambridge ; New York : Cambridge University Press, 2008.

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Details

Additional Authors

Borovkov, K. A. (Konstantin Aleksandrovich)

Description

xxix, 625 p. : ill.; 25 cm.

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.

Series Statement

Encyclopedia of mathematics and its applications ; [118]

Uniform Title

Encyclopedia of mathematics and its applications ; v. 118.

Subject

• Random walks (Mathematics)
• Asymptotic expansions

Note

• Series numbering from jacket

Bibliography (note)

• Includes bibliographical references (p. 611-623) and index.

Processing Action (note)

• committed to retain

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.

ISBN

• 9780521881173 (hbk.)
• 052188117X (hbk.)

LCCN

^^2008298018

OCLC

• 174130608
• SCSB-10029052

Owning Institutions

Harvard Library