Research Catalog
Asymptotic analysis of random walks : heavy-tailed distributions / A.A. Borovkov, K.A. Borovkov ; translated by O.B. Borovkova.
- 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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Status | Format | Access | Call Number | Item Location |
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Text | Request in advance | QA274.73 .B67 2008 | Off-site |
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
- 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