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Weak Convergence Methods and Singularly Perturbed Stochastic Control and Filtering Problems

  • Book
  • © 1990

Overview

Authors:
  1. Harold J. Kushner

    1. Division of Applied Mathematics, Brown University, Providence, USA

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Part of the book series: Systems & Control: Foundations & Applications (SCFA)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xvii
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  2. Weak Convergence

    • Harold J. Kushner
    Pages 1-16

  3. Stochastic Processes: Background

    • Harold J. Kushner
    Pages 17-43

  4. Controlled Stochastic Differential Equations

    • Harold J. Kushner
    Pages 45-60

  5. Controlled Singularly Perturbed Systems

    • Harold J. Kushner
    Pages 61-91

  6. Functional Occupation Measures and Average Cost per Unit Time Problems

    • Harold J. Kushner
    Pages 93-113

  7. The Nonlinear Filtering Problem

    • Harold J. Kushner
    Pages 115-150

  8. Weak Convergence: The Perturbed Test Function Method

    • Harold J. Kushner
    Pages 151-170

  9. Singularly Perturbed Wide-Band Noise Driven Systems

    • Harold J. Kushner
    Pages 171-190

  10. Stability Theory

    • Harold J. Kushner
    Pages 191-208

  11. Parametric Singularities

    • Harold J. Kushner
    Pages 209-217

  12. Back Matter

    Pages 219-233
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Keywords

About this book

The book deals with several closely related topics concerning approxima­ tions and perturbations of random processes and their applications to some important and fascinating classes of problems in the analysis and design of stochastic control systems and nonlinear filters. The basic mathematical methods which are used and developed are those of the theory of weak con­ vergence. The techniques are quite powerful for getting weak convergence or functional limit theorems for broad classes of problems and many of the techniques are new. The original need for some of the techniques which are developed here arose in connection with our study of the particular applica­ tions in this book, and related problems of approximation in control theory, but it will be clear that they have numerous applications elsewhere in weak convergence and process approximation theory. The book is a continuation of the author's long term interest in problems of the approximation of stochastic processes and its applications to problems arising in control and communication theory and related areas. In fact, the techniques used here can be fruitfully applied to many other areas. The basic random processes of interest can be described by solutions to either (multiple time scale) Ito differential equations driven by wide band or state dependent wide band noise or which are singularly perturbed. They might be controlled or not, and their state values might be fully observable or not (e. g. , as in the nonlinear filtering problem).

Authors and Affiliations

  • Division of Applied Mathematics, Brown University, Providence, USA

    Harold J. Kushner

Bibliographic Information

  • Book Title: Weak Convergence Methods and Singularly Perturbed Stochastic Control and Filtering Problems

  • Authors: Harold J. Kushner

  • Series Title: Systems & Control: Foundations & Applications

  • DOI: https://doi.org/10.1007/978-1-4612-4482-0

  • Publisher: Birkhäuser Boston, MA

  • eBook Packages: Springer Book Archive

  • Copyright Information: Birkhäuser Boston 1990

  • Hardcover ISBN: 978-0-8176-3437-7Published: 01 May 1990

  • Softcover ISBN: 978-1-4612-8838-1Published: 04 October 2011

  • eBook ISBN: 978-1-4612-4482-0Published: 06 December 2012

  • Series ISSN: 2324-9749

  • Series E-ISSN: 2324-9757

  • Edition Number: 1

  • Number of Pages: XVIII, 234

  • Topics: Probability Theory and Stochastic Processes, Systems Theory, Control

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