Numerical Methods for Stochastic Control Problems in Continuous Time / Edition 2

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Overview

astic control (and uncontrolled) problems of current interest, with di ffusion, jump-diffusion, or reflected diffusion models. There is a com plete coverage of the standard models as well as of ergodic and singul ar control, the types of reflected diffusion models that appear as mod els of controlled queuing networks, and the approximation of optimal n onlinear filters. There are two new chapters concerning problems with jump or variance control. The methods are powerful tools for determini stic problems as well, and there is a greatly expanded development of such problems, with particular emphasis on complex problems arising in the calculus of variations. Convergence is proved via the efficient p robabilistic methods of weak convergence theory. A weak local consiste ncy is the essential condition. The required background is surveyed, a nd there is an extensive development of methods of approximation compu tational algorithms. The book is written on two levels: algorithms and applications, and mathematical proofs. Thus, the ideas should be very accessible to a broad audience.

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Editorial Reviews

From the Publisher
"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
Booknews
Process models used are diffusions, jump-diffusions, or reflected diffusions of the type that occur in the majority of current applications. The required background in stochastic processes is surveyed, followed by extensive development of methods of approximation and a chapter devoted to computational techniques. The book is written on two levels, that of algorithms and applications, and that of mathematical development, making the methods used broadly accessible. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780387951393
  • Publisher: Springer New York
  • Publication date: 12/15/2000
  • Series: Stochastic Modelling and Applied Probability Series, #24
  • Edition description: 2nd ed. 2001
  • Edition number: 2
  • Pages: 476
  • Product dimensions: 6.45 (w) x 9.52 (h) x 1.11 (d)

Table of Contents

Review of Continuous Time Models.- Controlled Markov Chains.- Dynamic Programming Equations.- Markov Chain Approximation Method.- The Approximating Markov Chains.- Computational Methods.- The Ergodic Cost Problem.- Heavy Traffic and Singular Control.- Weak Convergence and the Characterization of Processes.- Convergence Proofs.- Convergence Proofs Continued.- Finite Time and Filtering Problems.- Controlled Variance and Jumps.- Problems from the Calculus of Variations: Finite Time Horizon.- Problems from the Calculus of Variations: Infinite Time Horizon.- The Viscosity Solution Approach.
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