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.
• 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
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; 7. Appendix.
'This 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. With its contents and style of presentation this attractive book will be very useful to postgraduate students in several areas, among them mathematics, statistics or probability, economics, biology or engineering.' Journal of the Royal Statistical Society