Stochastic Evolution Systems : Linear Theory and Applications to Non-Linear Filtering / by Boris L. Rozovsky, Sergey V. Lototsky.

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.

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.