Numerical Methods for Stochastic Control Problems in Continuous Time

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ISBN-13:
9780387951393
Einband:
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Erscheinungsdatum:
15.12.2000
Seiten:
492
Autor:
Paul G. Dupuis
Gewicht:
898 g
Format:
241x160x31 mm
Sprache:
Englisch
Beschreibung:

Stochastic control is a very active area of research. This monograph, written by two leading authorities in the field, has been updated to reflect the latest developments. It covers effective numerical methods for stochastic control problems in continuous time on two levels, that of practice and that of mathematical development. It is broadly accessible for graduate students and researchers.
Stochastic control is a very active area of research and this monograph written by two leading authorities in the field has been updated to reflect the latest developments. It covers effective numerical methods for stochastic control problems in continuous time on two levels, that of practice (algorithms and applications) and that of the mathematical development. It is broadly accessible for graduate students and researchers.
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.
Essentially all that is required of the approximations are some natural local consistency conditions. The approximations are consistent with standard methods of numerical analysis. The required background in 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.

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