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

• Main Authors: Rozovsky, Boris L. (Author, http://id.loc.gov/vocabulary/relators/aut), Lototsky, Sergey V. (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Edition: 2nd ed. 2018.
• Series: Probability Theory and Stochastic Modelling, 89
• Subjects: Probabilities.; Partial differential equations.; Functional analysis.; Electrical engineering.; Mathematical physics.; Probability Theory and Stochastic Processes.; Partial Differential Equations.; Functional Analysis.; Electrical Engineering.; Theoretical, Mathematical and Computational Physics.

This monograph, now in a thoroughly revised second edition, develops the theory of stochastic calculus in Hilbert spaces and applies the results to the study of generalized solutions of stochastic parabolic equations. The emphasis lies on second-order stochastic parabolic equations and their connect...

Table of Contents:

• 1 Examples and Auxiliary Results
• 2 Stochastic Integration in a Hilbert Space
• 3 Linear Stochastic Evolution Systems in Hilbert Spaces
• 4 Ito's Second Order Parabolic Equations
• 5 Ito's Partial Differential Equations and Diffusion Processes
• 6 Filtering, Interpolation and Extrapolation of Diffusion Processes
• 7 Hypoellipticity of Ito's Second Order Parabolic Equations
• 8 Chaos Expansion for Linear Stochastic Evolution Systems
• Notes
• References
• Index.