Stochastic Evolution Systems: Linear Theory and Applications to Non-Linear Filte

The Nile on
Stochastic Evolution Systems by Boris L. Rozovsky, Sergey V. Lototsky

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 emphasis lies on second-order stochastic parabolic equations and their connection to random dynamical systems.

FORMAT
Paperback LANGUAGE
English CONDITION
Brand New Publisher Description

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 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 book will appeal to anyone working in disciplines that require tools from stochastic analysis and PDEs, including pure mathematics, financial mathematics, engineering and physics.

Back Cover

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.

Table of Contents

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.

Review

"The book will be useful for those who are working in the area of applications of stochastic evolution systems in physics, biology and control theory, and require tools from stochastic analysis and partial differential equations." (Anatoliy Swishchuk, zbMATH 1434.60004, 2020)
"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)

Long Description

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.

Review Quote

"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 Br

Feature

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

Details ISBN3030069338 Author Sergey V. Lototsky Language English ISBN-10 3030069338 ISBN-13 9783030069339 Format Paperback Subtitle Linear Theory and Applications to Non-Linear Filtering DEWEY 515.353 Imprint Springer Nature Switzerland AG Place of Publication Cham Country of Publication Switzerland Translated from English Pages 330 Year 2018 Publication Date 2018-12-20 Short Title Stochastic Evolution Systems Edition 2nd Series Number 89 UK Release Date 2018-12-20 Publisher Springer Nature Switzerland AG Series Probability Theory and Stochastic Modelling Alternative 9783319948928 Audience Professional & Vocational Edition Description Second Edition 2018 Country of Origin NL Product Class Description Mathematics Illustrations 2 Illustrations, black and white
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