Limit Theorems for Large Deviations
Language: English
Published by Springer, Springer Okt 1991, 1991
- Softcover
- New
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This item is printed on demand - Print on Demand Titel. Neuware -1. The main notions.- 2. The main lemmas.- 2.1. General lemmas on the approximation of distribution of an arbitrary random variable by the normal distribution.- 2.2. Proof of lemmas 2.1-2.4.- 3. Theorems on large deviations for the distributions of sums of independent random variables.- 3.1. Theorems on large deviations under Bernstein's condition.- 3.2. A theorem of large deviations in terms of Lyapunov's fractions.- 4. Theorems of large deviations for sums of dependent random variables.- 4.1. Estimates of the kth order centered moments of random processes with mixing.- 4.2. Estimates of mixed cumulants of random processes with mixing.- 4.3. Estimates of cumulants of sums of dependent random variables.- 4.4. Theorems and inequalities of large deviations for sums of dependent random variables.- 5. Theorems of large deviations for polynomial forms, multiple stochastic integrals and statistical estimates.- 5.1. Estimates of cumulants and theorems of large deviations for polynomial forms, polynomial Pitman estimates and U-statistics.- 5.2. Cumulants of multiple stochastic integrals and theorems of large deviations.- 5.3. Large deviations for estimates of the spectrum of a stationary sequence.- 6. Asymptotic expansions in the zones of large deviations.- 6.1. Asymptotic expansion for distribution density of an arbitrary random variable.- 6.2. Estimates for characteristic functions.- 6.3. Asymptotic expansion in the Cramer zone for distribution density of sums of independent random variables.- 6.4. Asymptotic expansions in integral theorems with large deviations.- 7. Probabilities of large deviations for random vectors.- 7.1. General lemmas on large deviations for a random vector with regular behaviour of cumulants.- 7.2. Theorems on large deviations for sums of randomvectors and quadratic forms.- Appendices.- Appendix 1. Proof of inequalities for moments and Lyapunov's fractions.- Appendix 2. Proof of the lemma on the representation of cumulants.- Appendix 3. Leonov - Shiryaev's formula.- References.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 244 pp. Englisch.…
Seller Inventory # 9780792314752
- Title
- Limit Theorems for Large Deviations
- Author
- L. Saulis
- Publisher
- Springer, Springer Okt 1991
- Publication year
- 1991
- Condition
- Neu
- Binding
- Buch
- Language
- English
- ISBN 10
- 0792314751
- ISBN 13
- 9780792314752
- Item weight
- 535 grams
- Dimensions
- 241x160x18 mm
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buchversandmimpf2000
Emtmannsberg, BAYE, Germany
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