Book contents
- Frontmatter
- Contents
- Notation
- Introduction
- 1 Preliminaries
- 2 Random walks with jumps having no finite first moment
- 3 Random walks with jumps having finite mean and infinite variance
- 4 Random walks with jumps having finite variance
- 5 Random walks with semiexponential jump distributions
- 6 Large deviations on the boundary of and outside the Cramér zone for random walks with jump distributions decaying exponentially fast
- 7 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(Sn ≥ x)
- 8 On the asymptotics of the first hitting times
- 9 Integro-local and integral large deviation theorems for sums of random vectors
- 10 Large deviations in trajectory space
- 11 Large deviations of sums of random variables of two types
- 12 Random walks with non-identically distributed jumps in the triangular array scheme in the case of infinite second moment. Transient phenomena
- 13 Random walks with non-identically distributed jumps in the triangular array scheme in the case of finite variances
- 14 Random walks with dependent jumps
- 15 Extension of the results of Chapters 2–5 to continuous-time random processes with independent increments
- 16 Extension of the results of Chapters 3 and 4 to generalized renewal processes
- Bibliographic notes
- References
- Index
1 - Preliminaries
Published online by Cambridge University Press: 07 May 2010
Book contents
- Frontmatter
- Contents
- Notation
- Introduction
- 1 Preliminaries
- 2 Random walks with jumps having no finite first moment
- 3 Random walks with jumps having finite mean and infinite variance
- 4 Random walks with jumps having finite variance
- 5 Random walks with semiexponential jump distributions
- 6 Large deviations on the boundary of and outside the Cramér zone for random walks with jump distributions decaying exponentially fast
- 7 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(Sn ≥ x)
- 8 On the asymptotics of the first hitting times
- 9 Integro-local and integral large deviation theorems for sums of random vectors
- 10 Large deviations in trajectory space
- 11 Large deviations of sums of random variables of two types
- 12 Random walks with non-identically distributed jumps in the triangular array scheme in the case of infinite second moment. Transient phenomena
- 13 Random walks with non-identically distributed jumps in the triangular array scheme in the case of finite variances
- 14 Random walks with dependent jumps
- 15 Extension of the results of Chapters 2–5 to continuous-time random processes with independent increments
- 16 Extension of the results of Chapters 3 and 4 to generalized renewal processes
- Bibliographic notes
- References
- Index
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- Asymptotic Analysis of Random WalksHeavy-Tailed Distributions, pp. 1 - 79Publisher: Cambridge University PressPrint publication year: 2008