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

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

ISBN-10:
0387951393
ISBN-13:
9780387951393
Pub. Date:
12/15/2000
Publisher:
Springer New York

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Overview

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

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.

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
Pages: 476
Product dimensions: 6.10(w) x 9.25(h) x 0.04(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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