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.
General
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