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This treatment provides an exposition of discrete time dynamic processes evolving over an infinite horizon. Chapter 1 reviews some mathematical results from the theory of deterministic dynamical systems, with particular emphasis on applications to economics. The theory of irreducible Markov processes, especially Markov chains, is surveyed in Chapter 2. Equilibrium and long run stability of a dynamical system in which the law of motion is subject to random perturbations is the central theme of Chapters 3-5. A unified account of relatively recent results, exploiting splitting and contractions, that have found applications in many contexts is presented in detail. Chapter 6 explains how a random dynamical system may emerge from a class of dynamic programming problems. With examples and exercises, readers are guided from basic theory to the frontier of applied mathematical research.Read more
- Ideal for undergraduate and graduate courses on dynamic economics, Markov processes, Stochastic processes/probability
- Authors are internationally renowned for their work in this field
- Full of examples with many solutions, drawn from both applied mathematics and econometrics/statistics
Reviews & endorsements
As I turn the pages of this new book, I come to realize how lucky graduate students of today are.
Paul A. Samuelson, Nobel Laureate, Massachusetts Institute of TechnologySee more reviews
This book is a brilliant and clear synthesis of the known results on random processes in time. Any economist modeling the growth and cyclical behavior of an economy or of a smaller economic unit will need many of the results displayed and proved and will find no alternative as complete and clear. The numerous well-chosen problems are a bonus.
Kenneth J. Arrow, Nobel Laureate, Stanford University
This impressive and unique volume will be an excellent textbook as well as a valuable reference for economists and others interested in random dynamical systems. In addition to a rigorous treatment of the basic theory, the volume includes an introductory section on deterministic dynamical systems, an exposition of stochastic dynamic programming, and various applications to economic models, as well as many exercises and an appendix with basic mathematical background material.
Roy Radner, Stern School, New York University
This beautiful and elegantly written book by two world class scholars belongs on the bookshelf of any scholar who uses stochastic dynamical systems in his work. This includes ecologists, economists, mathematicians, mathematical biologists, statisticians, and many others.
William A. Brock, University of Wisconsin, Madison
Random Dynamical Systems is the product of the joint works of two masters, Rabi Bhattacharya and Mukul Majumdar, in mathematical statistics and mathematical economics, respectively. It presents the rigorous and yet lucid treatment of the theory of discrete time dynamical processes with applications to economics. I believe that this book will acquire the stature as the text of choice for students and researchers on this field for many years to come.
Kazuo Nishimura, Kyoto University
"This is a beautiful book. Although mostly oriented towards economic applications, there are sufficient references to and illustrations of other application scenarios to make this of interest to a far wider readership than merely econometricians. Engineers, statisticians, and physicists would find the material of interest and value."
International Statistical Review
"The material is well chosen, well structured and distributed in six chapter each consisting of sections. The presentation is rigorous and clear.... The book is written in a smooth style... The reviewer has all the arguments to recommend the book strongly not only to institutional libraries but also to anybody who is studying, teaching or using stochastic models."
Jordan Stoyanov, Newcastle University for the Journal of Royal Statistical Society
"The book is well written, giving complete proofs of theorems and providing numerous examples that not only demonstrate the applicability of the material, but also demonstrate the bizarre behavior possible in nonlinear systems. I believe that this book will be enjoyable to anyone having a background in Markov chains or an interest in nonlinear time series models."
Peter C. Kiessler, Clemson University, Journal of the American Statistician
"This book is very well written and it is a clear synthesis of the theory of discrete time dynamical processes with many applications to economics. In particular, the book contains a large number of examples and exercises, which in my opinion, make it a useful guide for students and also for researchers."
Maria J. Garrido-Atienza, Mathematical Reviews
11th Dec 2018 by Shuage
The Random Dynamical Systems: Theory and Applications is a fundamental and good book.
Review was not posted due to profanity×
- Date Published: January 2007
- format: Paperback
- isbn: 9780521532723
- length: 480 pages
- dimensions: 229 x 154 x 24 mm
- weight: 0.626kg
- availability: In stock
Table of Contents
1. Dynamical systems
2. Markov processes
3. Random dynamical systems
4. Random dynamical systems: special structures
5. Invariant distributions: estimations and computation
6. Discounted dynamic programming under uncertainty
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