Random Dynamical Systems

Surveys topics in the theory and applications of dynamical systems subject to random shocks.

Covers a range of topics related to the relatively recent literature on the theory and applications of dynamical systems subject to random shocks. It can serve as the basic text for courses on dynamic economics or stochastic processes, and is a valuable tool for further exploration.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.