Stochastic Controls: Hamiltonian Systems and Hjb Equations

Yong, Joingmin, and Yong, J, and Yong, Jiongmin

ISBN 10: 0387987231 / ISBN 13: 9780387987231

Published by Springer, New York, NY, 1999

About this Item

***INTERNATIONAL EDITION*** Read carefully before purchase: This book is the international edition in mint condition with the different ISBN and book cover design, the major content is printed in full English as same as the original North American edition. The book printed in black and white, generally send in twenty-four hours after the order confirmed. All shipments contain tracking numbers. Great professional textbook selling experience and expedite shipping service. Sewn binding. Cloth over boards. 464 p. Contains: Illustrations, black & white. Applications of Mathematics, 43. Audience: General/trade.

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Bibliographic Details

• Title: Stochastic Controls: Hamiltonian Systems and Hjb Equations
• Publisher: Springer, New York, NY
• Publication Date: 1999
• Language: English
• ISBN 10: 0387987231
• ISBN 13: 9780387987231
• Binding: Trade paperback
• Edition: First edition. 1999 ed.
• Condition: New in new dust jacket.

About this title

Synopsis

As is well known, Pontryagin's maximum principle and Bellman's dynamic programming are the two principal and most commonly used approaches in solving stochastic optimal control problems. * An interesting phenomenon one can observe from the literature is that these two approaches have been developed separately and independently. Since both methods are used to investigate the same problems, a natural question one will ask is the fol­ lowing: (Q) What is the relationship betwccn the maximum principlc and dy­ namic programming in stochastic optimal controls? There did exist some researches (prior to the 1980s) on the relationship between these two. Nevertheless, the results usually werestated in heuristic terms and proved under rather restrictive assumptions, which were not satisfied in most cases. In the statement of a Pontryagin-type maximum principle there is an adjoint equation, which is an ordinary differential equation (ODE) in the (finite-dimensional) deterministic case and a stochastic differential equation (SDE) in the stochastic case. The system consisting of the adjoint equa­ tion, the original state equation, and the maximum condition is referred to as an (extended) Hamiltonian system. On the other hand, in Bellman's dynamic programming, there is a partial differential equation (PDE), of first order in the (finite-dimensional) deterministic case and of second or­ der in the stochastic case. This is known as a Hamilton-Jacobi-Bellman (HJB) equation.

About the Author

Jiongmin Yong is a professor at the Department of Mathematics, Fudan University, Shanghai, China.