Research Catalog

Title

Stochastic controls : Hamiltonian systems and HJB equations / Jiongmin Yong, Xun Yu Zhou.

Author

Yong, J. (Jiongmin), 1958-

Publication

New York : Springer, [1999], ©1999.

Items in the Library & Off-site

Holdings

Details

Additional Authors

Zhou, Xun Yu.

Description

xx, 438 pages; 25 cm.

Summary

• "This book gives a self-contained and systematic exposition of the major optimal control theory for continuous-time stochastic diffusion processes, including the Pontryagin type maximum principle (MP) featuring second-order adjoint equations, the Bellman dynamic programming (DP) method via viscosity solution theory, and the Kalman linear-quadratic (LQ) models with indefinite cost functionals.
• A major feature of the controlled systems under consideration is that the controls enter into both the drifts and the diffusions, making it fundamentally different from the deterministic systems. The main theme of the book is on establishing relations between MP and DP, or essentially those between Hamiltonian systems and Hamilton-Jacobi-Bellman (HJB) equations."--BOOK JACKET.
• "This book can be used as a textbook for graduate students majoring in stochastic controls and applications. Some knowledge in measure theory and real analysis will be helpful. It can also serve as a reference for researchers in applied probability, control theory, operations research, physics, economics, and finance."--BOOK JACKET.

Series Statement

Applications of mathematics ; 43

Uniform Title

Applications of mathematics ; 43.

Subject

• Stochastic control theory
• Mathematical optimization
• Hamiltonian systems
• Hamilton-Jacobi equations

Bibliography (note)

• Includes bibliographical references (p. [401]-432) and index.

Contents

Ch. 1. Basic Stochastic Calculus -- Ch. 2. Stochastic Optimal Control Problems -- Ch. 3. Maximum Principle and Stochastic Hamiltonian Systems -- Ch. 4. Dynamic Programming and HJB Equations -- Ch. 5. The Relationship Between the Maximum Principle and Dynamic Programming -- Ch. 6. Linear Quadratic Optimal Control Problems -- Ch. 7. Backward Stochastic Differential Equations.

ISBN

0387987231 (acid-free paper)

LCCN

98055411

OCLC

ocm40559759

Owning Institutions

Columbia University Libraries