Asymptotic analysis of random walks heavy-tailed distributions
This book focuses on 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. Large deviation probabilities are of great interest in numerous ap...
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| Other Authors: | , |
| Format: | eBook |
| Language: | English |
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Cambridge
Cambridge University Press
2008
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| Series: | Encyclopedia of mathematics and its applications
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| Subjects: | |
| Online Access: | |
| Collection: | Cambridge Books Online - Collection details see MPG.ReNa |
Table of 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