PDF Ebook Random Dynamical Systems: Theory and Applications, by Rabi Bhattacharya, Mukul Majumdar
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Random Dynamical Systems: Theory and Applications, by Rabi Bhattacharya, Mukul Majumdar
PDF Ebook Random Dynamical Systems: Theory and Applications, by Rabi Bhattacharya, Mukul Majumdar
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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.
- Sales Rank: #2626322 in Books
- Brand: Brand: Cambridge University Press
- Published on: 2007-01-08
- Released on: 2007-03-29
- Original language: English
- Number of items: 1
- Dimensions: 8.98" h x .94" w x 5.98" l, 1.39 pounds
- Binding: Paperback
- 480 pages
- Used Book in Good Condition
Most helpful customer reviews
4 of 4 people found the following review helpful.
Serviceable
By Heraclitus Junior
This book is a serviceable treatment of dynamics in general. The first chapter covers discrete, deterministic dynamical systems and chaos. The second chapter is independent from the first and covers the general theory of Markov processes. The third chapter introduces (Markovian) random dynamical systems. The fourth chapter is on special cases of random dynamical systems. The fifth chapter covers some asymptotic stationarity results. The last chapter is on stochastic dynamic programming.
There are a few typos in the book and the way it has been typeset remind me of a draft rather than a final, polished textbook. The book is probably an OK entry point into the field if you have a solid background in undergraduate analysis and are already familiar with measure theory and probability. The exposition becomes quite dry and hard to follow as the book goes on. There are exercises in the book but they tend to be either too easy or too open ended. There are no solutions.
The book has definitely been written with economics in mind, almost all examples are derived from economics. Having said that, they're not particularly interesting examples. All in all, this is a good but not stellar book. It's hard to put my finger on it, but the book just didn't "excite" me enough.
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