Numerical Methods for Stochastic Control Problems in Continuous Time

Harold Kushner, Paul Dupuis - Collection Applications of mathematics

476 pages, parution le 30/12/2000 (2^eme édition)

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Résumé

This book presents a comprehensive development of effective numerical methods for stochastic control problems in continuous time. The process models are diffusions, jump-diffusions, or reflected diffusions of the type that occur in the majority of current applications. All the usual problem formulations are included, as well as those of more recent interest such as ergodic control, singular control and the types of reflected diffusions used as models of queuing networks.

Applications to complex deterministic problems are illustrated via application to a large class of problems from the calculus of variations. The general approach is known as the Markov Chain Approximation Method. The required background to stochastic processes is surveyed, there is an extensive development of methods of approximation, and a chapter is devoted to computational techniques.

The book is written on two levels, that of practice (algorithms and applications) and that of the mathematical development. Thus the methods and use should be broadly accessible. This update to the first edition will include added material on the control of the 'jump term' and the 'diffusion term.' There will be additional material on the deterministic problems, solving the Hamilton-Jacobi equations, for which the authors' methods are still among the most useful for many classes of problems. All of these topics are of great and growing current interest.

Sommaire

Introduction
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
References
Index
List of Symbols

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Harold Kushner, Paul Dupuis
Collection	Applications of mathematics
Parution	30/12/2000
Édition	2^eme édition
Nb. de pages	476
Format	16 x 24
Couverture	Relié
Poids	819g
Intérieur	Noir et Blanc
EAN13	9780387951393