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OverviewThis 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. Full Product DetailsAuthor: Boris L. Rozovsky , Sergey V. LototskyPublisher: Springer International Publishing AG Imprint: Springer International Publishing AG Edition: 2nd ed. 2018 Volume: 89 Weight: 0.688kg ISBN: 9783319948928ISBN 10: 331994892 Pages: 330 Publication Date: 15 October 2018 Audience: Professional and scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Language: English Table of Contents1 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.ReviewsA remarkable quality of this monograph is that the results are stated and proved with a great level of generality and rigor. The reader will find many interesting results, as well as lots of long and technical proofs ... . (Charles-Edouard Brehier, Mathematical Reviews, October, 2019) Author InformationBoris Rozovsky earned a Master’s degree in Probability and Statistics, followed by a PhD in Physical and Mathematical Sciences, both from the Moscow State (Lomonosov) University. He was Professor of Mathematics and Director of the Center for Applied Mathematical Sciences at the University of Southern California. Currently, he is the Ford Foundation Professor of Applied Mathematics at Brown University. Sergey Lototsky earned a Master’s degree in Physics in 1992 from the Moscow Institute of Physics and Technology, followed by a PhD in Applied Mathematics in 1996 from the University of Southern California. After a year-long post-doc at the Institute for Mathematics and its Applications and a three-year term as a Moore Instructor at MIT, he returned to the department of Mathematics at USC as a faculty member in 2000. He specializes in stochastic analysis, with emphasis on stochastic differential equation. He supervised more than 10 PhD students and had visiting positions at the Mittag-Leffler Institute in Sweden and at several universities in Israel and Italy. Tab Content 6Author Website:Countries AvailableAll regions |
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