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Numerical Methods for Stochastic Control Problems in Continuous Time

  • Harold J. Kushner
  • Paul G. Dupuis

Part of the Applications of Mathematics book series (SMAP, volume 24)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Harold J. Kushner, Paul G. Dupuis
    Pages 1-5
  3. Harold J. Kushner, Paul G. Dupuis
    Pages 7-33
  4. Harold J. Kushner, Paul G. Dupuis
    Pages 35-51
  5. Harold J. Kushner, Paul G. Dupuis
    Pages 53-65
  6. Harold J. Kushner, Paul G. Dupuis
    Pages 67-88
  7. Harold J. Kushner, Paul G. Dupuis
    Pages 89-149
  8. Harold J. Kushner, Paul G. Dupuis
    Pages 151-192
  9. Harold J. Kushner, Paul G. Dupuis
    Pages 193-216
  10. Harold J. Kushner, Paul G. Dupuis
    Pages 247-267
  11. Harold J. Kushner, Paul G. Dupuis
    Pages 269-301
  12. Harold J. Kushner, Paul G. Dupuis
    Pages 325-345
  13. Harold J. Kushner, Paul G. Dupuis
    Pages 347-410
  14. Harold J. Kushner, Paul G. Dupuis
    Pages 411-421
  15. Back Matter
    Pages 423-439

About this book

Introduction

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 prob­ lem formulations and sometimes surprising applications appear regularly. We have chosen forms of the models which cover the great bulk of the for­ mulations 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. Both the "drift" and the "variance" might be controlled. The cost functions might be any of the standard types: Discounted, stopped on first exit from a set, finite time, optimal stopping, average cost per unit time over the infinite time interval, and so forth.

Keywords

Markov chain Variation algorithms numerical analysis stochastic processes

Authors and affiliations

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

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4684-0441-8
  • Copyright Information Springer-Verlag New York 1992
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4684-0443-2
  • Online ISBN 978-1-4684-0441-8
  • Series Print ISSN 0172-4568
  • Buy this book on publisher's site