Stochastic Controls: Hamiltonian Systems and Hjb Equations - Couverture rigide

Yong, Jiongmin; Zhou, Xun Yu

Couverture rigide

ISBN 10 : 0387987231 ISBN 13 : 9780387987231

Editeur : Springer-Verlag New York Inc., 1999

Synopsis

This monograph unifies the two key approaches in solving optimal control problems. The book will be of interest to researchers and graduate students in applied probability, control engineering, and econometrics.

A propos du livre

À propos de l'auteur

Weijun Meng currently is engaging in her postdoctoral research at Academy of Mathematics and Systems Science, Chinese Academy of Sciences, P. R. China. She had a PhD degree from Shandong University, P. R. China. Her main research interests include stochastic optimal control, delayed stochastic systems and Stackelberg stochastic differential games. Jingtao Shi currently is a professor at Shandong University, P. R. China. He had a PhD degree from Shandong University, P. R. China. His main research interests include stochastic optimal control, differential games, leader-follower games, delayed stochastic systems, forward-backward stochastic systems and mathematical finance. Jiongmin Yong currently is a professor at University of Central Florida, USA. He had a PhD degree from Purdue University, USA. His main research interests include optimal control, stochastic differential/integral equations, and mathematical finance.

À propos de la quatrième de couverture

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.

Détails de l'édition

• Éditeur: Springer-Verlag New York Inc.
• Date d'édition: 1999
• Langue: anglais
• ISBN 10: 0387987231
• ISBN 13: 9780387987231
• Reliure: Relié
• Nombre de pages: 439
• Coordonnées du fabricant: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Allemagne