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.
• Physical Description: XVI, 330 p. 2 illus. online resource.
• ISBN: 9783319948935
• ISSN: 2199-3130 ;
• DOI: 10.1007/978-3-319-94893-5

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.