Stochastic Evolution Systems: Linear Theory and Applications to Non-linear Filtering (Mathematics and its Applications)

Rozovskii, B.L.

ISBN 10: 0792300378 / ISBN 13: 9780792300373

Editore: Springer, 1990

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0792300378 Fine/As New; Hardcover; This book is brand new and still sealed in the publisher's original shrinkwrap; Corners slightly "bumped" through the plastic; This book will be stored and delivered in a sturdy cardboard box with foam padding; Medium Format (8.5" - 9.75" tall); Orange covers with title in dark blue lettering; 1990, Springer-Verlag Publishing; 315 pages; "Stochastic Evolution Systems: Linear Theory and Applications to Non-linear Filtering (Mathematics and its Applications)," by B.L. Rozovskii.

Codice articolo SKU-U28ZH09002257

Dati bibliografici

• Titolo: Stochastic Evolution Systems: Linear Theory and Applications to Non-linear Filtering (Mathematics and its Applications)
• Editore: Springer
• Data di pubblicazione: 1990
• Lingua: Inglese
• ISBN 10: 0792300378
• ISBN 13: 9780792300373
• Rilegatura: Hardcover
• Condizione: Fine

Descrizione articolo

Riassunto

'Et moi, "'J si j'avait su comment en revcnir, One seMcc mathematics has rendered the je n'y semis point aile.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shclf next to the dusty canister labelled 'discarded non­ sense'. The series is divergent; therefore we may be able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non­ linearities 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.

Contenuti

1 Examples and Auxiliary Results.- 1.0. Introduction.- 1.1. Examples of Stochastic Evolution Systems.- 1.2. Measurability and Integrability in Banach Spaces.- 1.3. Martingales in ?1.- 1.4. Diffusion Processes.- 2 Stochastic Integration in a Hilbert Space.- 2.0. Introduction.- 2.1. Martingales and Local Martingales.- 2.2. Stochastic Integrals with Respect to Square Integrable Martingale.- 2.3. Stochastic Integrable with Respect to a Local Martingale.- 2.4. An Energy Equality in a Rigged Hilbert Space.- 3 Linear Stochastic Evolution Systems in Hilbert Spaces.- 3.0. Introduction.- 3.1. Coercive Systems.- 3.2. Dissipative Systems.- 3.3. Uniqueness and the Markov Property.- 3.4. The First Boundary Problem for Ito’s Partial Differential Equations.- 4 Ito’S Second Order Parabolic Equations.- 4.0. Introduction.- 4.1. The Cauchy Problem for Superparabolic Ito’s Second Order Parabolic Equations.- 4.2. The Cauchy Problem for Ito’s Second Order Equations.- 4.3. The Forward Cauchy Problem and the Backward One in Weighted Sobolev Spaces.- 5 Ito’s Partial Differential Equations and Diffusion Processes.- 5.0. Introduction.- 5.1. The Method of Stochastic Characteristics.- 5.2. Inverse Diffusion Processes, the Method of Variation of Constants and the Liouville Equations.- 5.3. A Representation of a Density-valued Solution.- 6 Filtering Interpolation and Extrapolation of Diffusion Processes.- 6.0. Introduction.- 6.1. Bayes’ Formula and the Conditional Markov Property.- 6.2. The Forward Filtering Equation.- 6.3. The Backward Filtering Equation Interpolation and Extrapolation.- 7 Hypoellipticity of Ito’s Second Order Parabolic Equations.- 7.0. Introduction.- 7.1. Measure-valued Solution and Hypoellipticity under Generalized Hörmander’s Condition.- 7.2. The Filtering Transition Density and a Fundamental Solution of the Filtering Equation in Hypoelliptic and Superparabolic Cases.- Notes.- References.