Limit Theorems on Large Deviations for Markov Stochastic Processes (Mathematics and its Applications, 38)

Wentzell, A.D.

ISBN 10: 0792301439 ISBN 13: 9780792301431
Published by Springer, 1990
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One service mathematics has rendered the 'Et BIOi. .... si j'avait su comment en revenir. human race. It has put common sense back je n'y serais point aile.' Jules Verne where it belongs. on the topmost shelf next to the dusty canister labelled 'discarded non­ The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O. Heaviside Math@matics is a tool for thought. A highly necessary tool in a world where both feedback and non­ Iinearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com­ puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

Synopsis: Limit theorems for stochastic processes are the natural modern generalization of limit theorems for sums of independent random variables. This volume (translated from the 1986 Russian original) examines this generalization, considering wide classes of families of stochastic processes instead of those based on independent random variables. Annotatio

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Title: Limit Theorems on Large Deviations for ...
Publisher: Springer
Publication Date: 1990
Binding: Hardcover
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A. D. Wentzell
Published by Springer Netherlands, 1990
ISBN 10: 0792301439 ISBN 13: 9780792301431
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Condition: Sehr gut. Zustand: Sehr gut | Sprache: Englisch | Produktart: Bücher | One service mathematics has rendered the 'Et BIOi. . si j'avait su comment en revenir. human race. It has put common sense back je n'y serais point aile.' Jules Verne where it belongs. on the topmost shelf next to the dusty canister labelled 'discarded non­ The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O. Heaviside Math@matics is a tool for thought. A highly necessary tool in a world where both feedback and non­ Iinearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics . .'; 'One service logic has rendered com­ puter science . .'; 'One service category theory has rendered mathematics . .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series. Seller Inventory # 1867981/202

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A.D. Wentzell
Published by Springer Netherlands, 1990
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Gebunden. Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. 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 proc. Seller Inventory # 5965680

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A. D. Wentzell
Published by Springer, Springer Okt 1990, 1990
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Buch. Condition: Neu. 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

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