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 connection to random dynamical systems. The authors further explore applications to the theory of optimal non-linear filtering, prediction, and smoothing of partially observed diffusion processes. The new edition now also includes a chapter on chaos expansion for linear stochastic evolution systems.
This book will appeal to anyone working in disciplines that require tools from stochastic analysis and PDEs, including pure mathematics, financial mathematics, engineering and physics.
Author(s): Boris L. Rozovsky, Sergey V. Lototsky
Series: Probability Theory and Stochastic Modelling, Vol. 89
Edition: 2
Publisher: Springer
Year: 2018
Language: English
Pages: 340
Tags: Stochastic Analysis
Front Matter ....Pages i-xvi
Examples and Auxiliary Results (Boris L. Rozovsky, Sergey V. Lototsky)....Pages 1-37
Stochastic Integration in a Hilbert Space (Boris L. Rozovsky, Sergey V. Lototsky)....Pages 39-84
Linear Stochastic Evolution Systems in Hilbert Spaces (Boris L. Rozovsky, Sergey V. Lototsky)....Pages 85-122
Itô’s Second-Order Parabolic Equations (Boris L. Rozovsky, Sergey V. Lototsky)....Pages 123-170
Itô’s Partial Differential Equations and Diffusion Processes (Boris L. Rozovsky, Sergey V. Lototsky)....Pages 171-212
Filtering, Interpolation and Extrapolation of Diffusion Processes (Boris L. Rozovsky, Sergey V. Lototsky)....Pages 213-241
Hypoellipticity of Itô’s Second Order Parabolic Equations (Boris L. Rozovsky, Sergey V. Lototsky)....Pages 243-278
Chaos Expansion for Linear Stochastic Evolution Systems (Boris L. Rozovsky, Sergey V. Lototsky)....Pages 279-314
Back Matter ....Pages 315-330
