Overview
- Provides a self-contained development of the theory of generalized solutions of stochastic parabolic equations
- Explores equations of optimal non-linear filtering, interpolation, and extrapolation of diffusion processes in detail
- Establishes various connections between diffusions and linear stochastic parabolic equations
Part of the book series: Probability Theory and Stochastic Modelling (PTSM, volume 89)
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Table of contents (8 chapters)
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Front Matter
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Back Matter
Keywords
- MSC (2010): 60H15, 35R60
- Boundary value problem
- Markov property
- Martingale
- Sobolev space
- diffusion process
- filtering problem
- local martingale
- partial differential equation
- backward diffusion equation
- chaos solution of parabolic equations
- interpolation
- extrapolation
- Hormander's condition in filtering
- stochastic characteristics
- stochastic integration in Hilbert space
- partial differential equations
About this book
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.
Reviews
“A 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 Bréhier, Mathematical Reviews, October, 2019)
Authors and Affiliations
About the authors
Boris 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.
Bibliographic Information
Book Title: Stochastic Evolution Systems
Book Subtitle: Linear Theory and Applications to Non-Linear Filtering
Authors: Boris L. Rozovsky, Sergey V. Lototsky
Series Title: Probability Theory and Stochastic Modelling
DOI: https://doi.org/10.1007/978-3-319-94893-5
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2018
Hardcover ISBN: 978-3-319-94892-8Published: 15 October 2018
Softcover ISBN: 978-3-030-06933-9Published: 20 December 2018
eBook ISBN: 978-3-319-94893-5Published: 03 October 2018
Series ISSN: 2199-3130
Series E-ISSN: 2199-3149
Edition Number: 2
Number of Pages: XVI, 330
Number of Illustrations: 2 b/w illustrations
Additional Information: 1st ed. translated from Russian by A. Yarkho, published under Rozovskii, B.L. in the series Mathematics and Its Applications vol. 35, Kluwer Academic Publishers. Original Russian language edition published by Nauka Publishers, Moscow, 1983
Topics: Probability Theory and Stochastic Processes, Partial Differential Equations, Functional Analysis, Electrical Engineering, Theoretical, Mathematical and Computational Physics