Limit Theorems on Large Deviations for Markov Stochastic Processes
Language: English
Published by Springer, Springer Okt 1990, 1990
- Hardcover
- New
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This item is printed on demand - Print on Demand Titel. Neuware -0.1 Problems on large deviations for stochastic processes.- 0.2 Two opposite types of behaviour of probabilities of large deviations.- 0.3 Rough theorems on large deviations; the action functional.- 0.4 Survey of work on large deviations for stochastic processes.- 0.5 The scheme for obtaining rough theorems on large deviations.- 0.6 The expression: k ( ) S ( ) is the action functional uniformly over a specified class of initial points.- 0.7 Chapters 3 - 6: a survey.- 0.8 Numbering.- 1. General Notions, Notation, Auxiliary Results.- 1.1. General notation. Legendre transformation.- 1.2. Compensators. Lévy measures.- 1.3. Compensating operators of Markov processes.- 2. Estimates Associated with the Action Functional for Markov Processes.- 2.1. The action functional.- 2.2. Derivation of the lower estimate for the probability of passing through a tube.- 2.3. Derivation of the upper estimate for the probability of going far from the sets$$ {{Phi }_{{{{x}_{0}};left[ {0,T}ight]}}}left( iight),{{bar{Phi }}_{{{{x}_{0}};left[ {0,T}ight]}}}left( iight) $$.- 2.4. The truncated action functional and the estimates associated with it.- 3. The Action Functional for Families of Markov Processes.- 3.1. The properties of the functional$$ {{S}_{{{{T}_{1}},{{T}_{2}}}}}left( phiight) $$.- 3.2. Theorems on the action functional for families of Markov processes in Rr. The case of finite exponential moments.- 3.3. Transition to manifolds. Action functional theorems associated with truncated cumulants.- 4. Special Cases.- 4.1. Conditions A - E of 3.1. - 3.3.- 4.2. Patterns of processes with frequent small jumps. The cases of very large deviations, not very large deviations, and super-large deviations.- 4.3. The case of very large deviations.- 4.4. Thecase of not very large deviations.- 4.5. Some other patterns of not very large deviations.- 4.6. The case of super-large deviations.- 5. Precise Asymptotics for Large Deviations.- 5.1. The case of the Wiener process.- 5.2. Processes with frequent small jumps.- 6. Asymptotics of the Probability of Large Deviations Due to Large Jumps of a Markov Process.- 6.1. Conditions imposed on the family of processes. Auxiliary results.- 6.2. Main theorems.- 6.3. Applications to sums of independent random variables.- References.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 198 pp. Englisch.…
Seller Inventory # 9780792301431
- Title
- Limit Theorems on Large Deviations for Markov Stochastic Processes
- Author
- A. D. Wentzell
- Publisher
- Springer, Springer Okt 1990
- Publication year
- 1990
- Condition
- Neu
- Binding
- Buch
- Language
- English
- ISBN 10
- 0792301439
- ISBN 13
- 9780792301431
- Item weight
- 468 grams
- Dimensions
- 241x160x16 mm
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Emtmannsberg, BAYE, Germany
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