Order from a Major Online Bookstore
Ultimate Book Price Comparison Engine
Save Your Time And Money
| AnyBook4Less.com | Order from a Major Online Bookstore |
|
| Home | Store List | FAQ | Contact Us | | ||
| Ultimate Book Price Comparison Engine Save Your Time And Money |
||
 |
Title: Stochastic Controls: Hamiltonian Systems and Hjb Equations (Applications of Mathematics, 43) by Jiongmin Yong, Xun Yu Zhou ISBN: 0-387-98723-1 Publisher: Springer Verlag Pub. Date: June, 1999 Format: Hardcover Volumes: 1 List Price(USD): $92.00 |
Average Customer Rating: 4 (1 review)
Rating: 4
Summary: Wow: a general solution to stochastic control problems!
Comment: This book covers general stochastic control more thoroughly than any other book I could find.
This is *not* a book on numerical methods. It is also not on the cases which yield closed-form solutions: there is a chapter on LQG problems, but for the most part, this book focuses on the general theory of stochastic controls -- which are not the easiest things to solve in general, as you may know. The book handles only diffusion processes with perfect knowledge of the past and present (natural filtration). If these sound like what you want, I doubt there's a more thorough treatment.
It starts with a chapter on preliminaries of prob. spaces and stoch. processes and the Ito integral. After that, the book briefly addresses deterministic problems in order to compare solution methods to the stoch. approaches. It approaches the problems using a stochastic maximum principle and a stochastic Hamiltonian system, and also from a dynamic programming point of view using HJB equations. The authors attempt to show the relationship between the two approaches.
This book is technically rigorous. Though it claims to be self-contained, the reader should certainly be familiar with functional analysis and stochastic processes.
The authors try to keep the solutions as general as possible, handling non-smooth cases as well as smooth ones. This is fine, except that they don't emphasize well enough (I thought), for instance, that the solutions are much simpler when functions are well behaved on convex bodies (it's mentioned as a note on p. 120), or when diffusions are not dependent on controls, and such.
Because of this tendency to present one solution which will handle any case, it could sometimes be difficult to figure out what all the terms are. In the end, it all works out. Each chapter ends with a few pages of "historical background": who did what piece of the theory when, with an excellent list of references. (I found the originals useful to help explain things, on occasion, especially to see simpler ways to do simpler cases)
Altogether, a very thorough piece on general solutions to stochastic control! I was quite impressed.
 |
Title: Limit Theorems for Stochastic Processes by Albert Nikolaevich Shiriaev, Jean Jacod, N. Shiryaev, K. Erik Franzen ISBN: 3540439323 Publisher: Springer Verlag Pub. Date: 16 December, 2002 List Price(USD): $153.00 |
 |
Title: Numerical Methods for Stochastic Control Problems in Continuous Time (Applications of Mathematics, Vol 24) by Harold J. Kushner, Paul Dupuis ISBN: 0387951393 Publisher: Springer Verlag Pub. Date: May, 2001 List Price(USD): $89.95 |
 |
Title: A Second Course in Stochastic Processes by Samuel Karlin, Howard Taylor ISBN: 0123986508 Publisher: Academic Press Pub. Date: 28 April, 1981 List Price(USD): $79.95 |
 |
Title: Methods of Mathematical Finance by Ioannis Karatzas, Steven E. Shreve ISBN: 0387948392 Publisher: Springer Verlag Pub. Date: 13 August, 1998 List Price(USD): $79.95 |
 |
Title: Brownian Motion and Stochastic Calculus (Graduate Texts in Mathematics, Vol 113) by Ioannis Karatzas, Steven E. Shreve, Steven E. Shreve ISBN: 0387976558 Publisher: Springer Verlag Pub. Date: 20 June, 1997 List Price(USD): $59.95 |
Thank you for visiting www.AnyBook4Less.com and enjoy your savings!
Copyright� 2001-2021 Send your comments
