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Stochastic Evolution Systems

Linear Theory and Applications to Non-Linear Filtering

  • Boris L. Rozovsky
  • Sergey V. Lototsky

Part of the Probability Theory and Stochastic Modelling book series (PTSM, volume 89)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Boris L. Rozovsky, Sergey V. Lototsky
    Pages 1-37
  3. Boris L. Rozovsky, Sergey V. Lototsky
    Pages 39-84
  4. Boris L. Rozovsky, Sergey V. Lototsky
    Pages 85-122
  5. Boris L. Rozovsky, Sergey V. Lototsky
    Pages 123-170
  6. Boris L. Rozovsky, Sergey V. Lototsky
    Pages 171-212
  7. Boris L. Rozovsky, Sergey V. Lototsky
    Pages 213-241
  8. Boris L. Rozovsky, Sergey V. Lototsky
    Pages 243-278
  9. Boris L. Rozovsky, Sergey V. Lototsky
    Pages 279-314
  10. Back Matter
    Pages 315-330

About this book

Introduction

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.

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

Authors and affiliations

  • Boris L. Rozovsky
    • 1
  • Sergey V. Lototsky
    • 2
  1. 1.Division of Applied MathematicsBrown UniversityProvidenceUSA
  2. 2.Department of MathematicsUniversity of Southern CaliforniaLos AngelesUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-94893-5
  • Copyright Information Springer Nature Switzerland AG 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-94892-8
  • Online ISBN 978-3-319-94893-5
  • Series Print ISSN 2199-3130
  • Series Online ISSN 2199-3149
  • Buy this book on publisher's site
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