Asymptotic Analysis of Random Walks

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März 2008



A comprehensive monograph presenting a unified systematic exposition of the large deviations theory for heavy-tailed random walks.


Introduction; 1. Preliminaries; 2. Random walks with jumps having no finite first moment; 3. Random walks with finite mean and infinite variance; 4. Random walks with jumps having finite variance; 5. Random walks with semiexponential jump distributions; 6. Random walks with exponentially decaying distributions; 7. Asymptotic properties of functions of distributions; 8. On the asymptotics of the first hitting times; 9. Large deviation theorems for sums of random vectors; 10. Large deviations in the space of trajectories; 11. Large deviations of sums of random variables of two types; 12. Non-identically distributed jumps with infinite second moments; 13. Non-identically distributed jumps with finite variances; 14. Random walks with dependent jumps; 15. Extension to processes with independent increments; 16. Extensions to generalised renewal processes; Bibliographic notes; Index of notations; Bibliography.


Alexander Borovkov works at the Sobolev Institute of Mathematics in Novosibirsk. Konstantin Borovkov is a staff member in the Department of Mathematics and Statistics at the University of Melbourne.


'This book is a worthy tribute to the amazing fecundity of the structure of random walks!' Mathematical Reviews '... an up-to-date, unified and systematic exposition of the field. Most of the results presented are appearing in a monograph for the first time and a good proportion of them were obtained by the authors. ... The book presents some beautiful and useful mathematics that may attract a number of probabilists to the large deviations topic in probability.' EMS Newsletter
EAN: 9780521881173
ISBN: 052188117X
Untertitel: 'Encyclopedia of Mathematics an'. New. Sprache: Englisch.
Erscheinungsdatum: März 2008
Seitenanzahl: 656 Seiten
Format: gebunden
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