Numerical Methods for Stochastic Control Problems in Continuous Time

  • Harold J. Kushner
  • Paul Dupuis

Part of the Stochastic Modelling and Applied Probability book series (SMAP, volume 24)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Harold J. Kushner, Paul Dupuis
    Pages 1-6
  3. Harold J. Kushner, Paul Dupuis
    Pages 7-34
  4. Harold J. Kushner, Paul Dupuis
    Pages 35-52
  5. Harold J. Kushner, Paul Dupuis
    Pages 53-66
  6. Harold J. Kushner, Paul Dupuis
    Pages 67-88
  7. Harold J. Kushner, Paul Dupuis
    Pages 89-151
  8. Harold J. Kushner, Paul Dupuis
    Pages 153-189
  9. Harold J. Kushner, Paul Dupuis
    Pages 191-214
  10. Harold J. Kushner, Paul Dupuis
    Pages 245-265
  11. Harold J. Kushner, Paul Dupuis
    Pages 267-299
  12. Harold J. Kushner, Paul Dupuis
    Pages 325-345
  13. Harold J. Kushner, Paul Dupuis
    Pages 347-366
  14. Harold J. Kushner, Paul Dupuis
    Pages 367-400
  15. Harold J. Kushner, Paul Dupuis
    Pages 401-442
  16. Back Matter
    Pages 455-476

About this book

Introduction

Changes in the second edition. The second edition differs from the first in that there is a full development of problems where the variance of the diffusion term and the jump distribution can be controlled. Also, a great deal of new material concerning deterministic problems has been added, including very efficient algorithms for a class of problems of wide current interest. This book is concerned with numerical methods for stochastic control and optimal stochastic control problems. The random process models of the controlled or uncontrolled stochastic systems are either diffusions or jump diffusions. Stochastic control is a very active area of research and new problem formulations and sometimes surprising applications appear regu­ larly. We have chosen forms of the models which cover the great bulk of the formulations of the continuous time stochastic control problems which have appeared to date. The standard formats are covered, but much emphasis is given to the newer and less well known formulations. The controlled process might be either stopped or absorbed on leaving a constraint set or upon first hitting a target set, or it might be reflected or "projected" from the boundary of a constraining set. In some of the more recent applications of the reflecting boundary problem, for example the so-called heavy traffic approximation problems, the directions of reflection are actually discontin­ uous. In general, the control might be representable as a bounded function or it might be of the so-called impulsive or singular control types.

Keywords

Calculus of Variations Markov chain Stochastic processes Variance algorithms filtering problem stochastic process

Authors and affiliations

  • Harold J. Kushner
    • 1
  • Paul Dupuis
    • 1
  1. 1.Division of Applied MathematicsBrown UniversityProvidenceUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4613-0007-6
  • Copyright Information Springer-Verlag New York 2001
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-6531-3
  • Online ISBN 978-1-4613-0007-6
  • Series Print ISSN 0172-4568
  • Series Online ISSN 2197-439X
  • About this book