Stochastic Evolution Systems
Linear Theory and Applications to Non-linear Filtering
(Sprache: Englisch)
Covering the general theory of linear stochastic evolution systems with unbounded drift and diffusion operators, this book sureys Ito's second-order parabolic equations and explores filtering problems for processes whose trajectories can be described by them.
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Produktinformationen zu „Stochastic Evolution Systems “
Covering the general theory of linear stochastic evolution systems with unbounded drift and diffusion operators, this book sureys Ito's second-order parabolic equations and explores filtering problems for processes whose trajectories can be described by them.
Klappentext zu „Stochastic Evolution Systems “
'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.
Inhaltsverzeichnis zu „Stochastic Evolution Systems “
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 andthe 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.
Bibliographische Angaben
- Autor: B. L. Rozovskii
- 2012, 1990., 315 Seiten, Maße: 23,5 cm, Kartoniert (TB), Englisch
- Verlag: Springer Netherlands
- ISBN-10: 9401057036
- ISBN-13: 9789401057035
Sprache:
Englisch
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