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Numerical Methods for Stochastic Control Problems in Continuous Time

  • Book
  • © 1992

Overview

Authors:
  1. Harold J. Kushner

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

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    You can also search for this author in PubMed   Google Scholar

  2. Paul G. Dupuis

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

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    You can also search for this author in PubMed   Google Scholar

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

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Table of contents (15 chapters)

  1. Front Matter

    Pages i-ix
    Download chapter PDF

  2. Introduction

    • Harold J. Kushner, Paul G. Dupuis
    Pages 1-5

  3. Review of Continuous Time Models

    • Harold J. Kushner, Paul G. Dupuis
    Pages 7-33

  4. Controlled Markov Chains

    • Harold J. Kushner, Paul G. Dupuis
    Pages 35-51

  5. Dynamic Programming Equations

    • Harold J. Kushner, Paul G. Dupuis
    Pages 53-65

  6. The Markov Chain Approximation Method: Introduction

    • Harold J. Kushner, Paul G. Dupuis
    Pages 67-88

  7. Construction of the Approximating Markov Chain

    • Harold J. Kushner, Paul G. Dupuis
    Pages 89-149

  8. Computational Methods for Controlled Markov Chains

    • Harold J. Kushner, Paul G. Dupuis
    Pages 151-192

  9. The Ergodic Cost Problem: Formulation and Algorithms

    • Harold J. Kushner, Paul G. Dupuis
    Pages 193-216

  10. Heavy Traffic and Singular Control Problems: Examples and Markov Chain Approximations

    • Harold J. Kushner, Paul G. Dupuis
    Pages 217-245

  11. Weak Convergence and the Characterization of Processes

    • Harold J. Kushner, Paul G. Dupuis
    Pages 247-267

  12. Convergence Proofs

    • Harold J. Kushner, Paul G. Dupuis
    Pages 269-301

  13. Convergence for Reflecting Boundaries, Singular Control and Ergodic Cost Problems

    • Harold J. Kushner, Paul G. Dupuis
    Pages 303-323

  14. Finite Time Problems and Nonlinear Filtering

    • Harold J. Kushner, Paul G. Dupuis
    Pages 325-345

  15. Problems from the Calculus of Variations

    • Harold J. Kushner, Paul G. Dupuis
    Pages 347-410

  16. The Viscosity Solution Approach to Proving Convergence of Numerical Schemes

    • Harold J. Kushner, Paul G. Dupuis
    Pages 411-421

  17. Back Matter

    Pages 423-439
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Keywords

About this book

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.

Authors and Affiliations

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

    Harold J. Kushner, Paul G. Dupuis

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