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Controlled Markov Processes & Viscosity Solutions

Controlled Markov Processes & Viscosity Solutions Cover

 

Synopses & Reviews

Publisher Comments:

This book is intended as an introduction to optimal stochastic control for continuous time Markov processes and to the theory of viscosity solutions. Stochastic control problems are treated using the dynamic programming approach. The authors approach stochastic control problems by the method of dynamic programming. The fundamental equation of dynamic programming is a nonlinear evolution equation for the value function. For controlled Markov diffusion processes, this becomes a nonlinear partial differential equation of second order, called a Hamilton-Jacobi-Bellman (HJB) equation. Typically, the value function is not smooth enough to satisfy the HJB equation in a classical sense. Viscosity solutions provide framework in which to study HJB equations, and to prove continuous dependence of solutions on problem data. The theory is illustrated by applications from engineering, management science, and financial economics. In this second edition, new material on applications to mathematical finance has been added. Concise introductions to risk-sensitive control theory, nonlinear H-infinity control and differential games are also included. Review of the earlier edition: "This book is highly recommended to anyone who wishes to learn the dinamic principle applied to optimal stochastic control for diffusion processes. Without any doubt, this is a fine book and most likely it is going to become a classic on the area... ." SIAM Review, 1994

Book News Annotation:

Full of examples drawn from engineering, management science, and financial economics, this introductory text contains chapters on deterministic optimal control, viscosity solutions, classical solutions to optimal control of Markov processes, controlled Markov diffusions, logarithmic transformations, single perturbations, singular stochastic control, and finite-difference numerical approximations. Historical remarks conclude each chapter.
Annotation c. Book News, Inc., Portland, OR (booknews.com)

Table of Contents

Deterministic Optimal Control.-Viscosity Solutions.- Optimal Control of Markov Processes: Classical Solutions.- Controlled Markov Diffusions in IR .-Viscosity Solutions: Second-Order Case.- Logarithmic Transformations.- Singular Perturbations.- Singular Stochastic Control.- Finite-Difference Numerical Approximations.- Appendix A thru E.-References.- Index.

Product Details

ISBN:
9780387979274
Publisher:
Springer
Subject:
Probability
Author:
Fleming, Wendell Helms
Author:
Soner, H. Mete
Author:
Fleming, Wendell H.
Author:
Soner, H. M.
Subject:
Markov processes
Subject:
Stochastic control theory.
Subject:
Probability & Statistics - General
Subject:
Mathematics | Probability and Statistics
Copyright:
Edition Number:
1
Series:
Springer Series in Statistics
Series Volume:
25
Publication Date:
December 1992
Binding:
Hardcover
Language:
English
Illustrations:
Y
Pages:
452
Dimensions:
9.21x6.14x1.06 in. 1.78 lbs.

Related Subjects

Science and Mathematics » Mathematics » Probability and Statistics » General
Science and Mathematics » Mathematics » Probability and Statistics » Statistics

Controlled Markov Processes & Viscosity Solutions
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Product details 452 pages Springer-Verlag New York, Incorporated - English 9780387979274 Reviews:
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