Limit Theorems on Large Deviations for Markov Stochastic Processes

Language: English

Published by Springer Netherlands, 1990

0792301439 / 9780792301431

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Druck auf Anfrage Neuware - Printed after ordering - 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$$ {{Phi }_{{{{x}_{0}};left[ {0,T} right]}}}left( i right),{{bar{Phi }}_{{{{x}_{0}};left[ {0,T} right]}}}left( i right) $$.- 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$$ {{S}_{{{{T}_{1}},{{T}_{2}}}}}left( phi right) $$.- 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 of3.1.3.3.- 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.…

Seller Inventory # 9780792301431

Title
Limit Theorems on Large Deviations for Markov Stochastic Processes
Author
A. D. Wentzell
Publisher
Springer Netherlands
Publication year
1990
Condition
Neu
Binding
Buch
Language
English
ISBN 10
0792301439
ISBN 13
9780792301431
Item weight
416 grams
Dimensions
241x160x16 mm

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