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Field name	Details
Dewey Class	519.2
Title	Stochastic Evolution Systems ([EBook]) : Linear Theory and Applications to Non-linear Filtering / by B. L. Rozovskii.
Author	Rozovskii, Boris L.
Other name(s)	SpringerLink (Online service)
Publication	Dordrecht : Springer Netherlands , 1990.
Physical Details	XVIII, 315 pages. : online resource.
Series	Mathematics and its applications. Soviet series 0169-6378 ; ; 35
ISBN	9789401138307
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-94-011-3830-7
Links to Related Works	Subject References: Electrical engineering . Mathematics . Partial differential equations . Physics . Probabilities . Probability theory and stochastic processes . Theoretical, Mathematical and Computational Physics . Authors: Rozovskii, Boris L. . Corporate Authors: SpringerLink (Online service) . Series: Mathematics and its applications. Soviet series . Classification: 519.2 .

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Stochastic Evolution Systems: Linear Theory and Applications to Non-linear Filtering /

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