Skip to main content
  • Textbook
  • © 2001

Numerical Methods for Stochastic Control Problems in Continuous Time

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

Buy it now

Buying options

eBook USD 79.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 99.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 139.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

This is a preview of subscription content, access via your institution.

Table of contents (17 chapters)

  1. Front Matter

    Pages i-xii
  2. Introduction

    • Harold J. Kushner, Paul Dupuis
    Pages 1-6
  3. Review of Continuous Time Models

    • Harold J. Kushner, Paul Dupuis
    Pages 7-34
  4. Controlled Markov Chains

    • Harold J. Kushner, Paul Dupuis
    Pages 35-52
  5. Dynamic Programming Equations

    • Harold J. Kushner, Paul Dupuis
    Pages 53-66
  6. The Markov Chain Approximation Method: Introduction

    • Harold J. Kushner, Paul Dupuis
    Pages 67-88
  7. Construction of the Approximating Markov Chain

    • Harold J. Kushner, Paul Dupuis
    Pages 89-151
  8. Computational Methods for Controlled Markov Chains

    • Harold J. Kushner, Paul Dupuis
    Pages 153-189
  9. The Ergodic Cost Problem: Formulation and Algorithms

    • Harold J. Kushner, Paul Dupuis
    Pages 191-214
  10. Weak Convergence and the Characterization of Processes

    • Harold J. Kushner, Paul Dupuis
    Pages 245-265
  11. Convergence Proofs

    • Harold J. Kushner, Paul Dupuis
    Pages 267-299
  12. Finite Time Problems and Nonlinear Filtering

    • Harold J. Kushner, Paul Dupuis
    Pages 325-345
  13. Controlled Variance and Jumps

    • Harold J. Kushner, Paul Dupuis
    Pages 347-366
  14. Problems from the Calculus of Variations: Finite Time Horizon

    • Harold J. Kushner, Paul Dupuis
    Pages 367-400
  15. Problems from the Calculus of Variations: Infinite Time Horizon

    • Harold J. Kushner, Paul Dupuis
    Pages 401-442
  16. Back Matter

    Pages 455-476

About this book

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 reguĀ­ 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 discontinĀ­ 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

Reviews

"The second edition of this acclaimed book from Springer-Verlag has the latest theoretical and practical information on solving stochastic control problems. Including proofs and algorithms using diffusion, jump-diffusion, and other process models, the authors help make randomness a little less scary."
Amazon.com Delivers Mathematics and Statistics e-bulletin, July 2001

Authors and Affiliations

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

    Harold J. Kushner, Paul Dupuis

Bibliographic Information

Buy it now

Buying options

eBook USD 79.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 99.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 139.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access