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Random Dynamical Systems

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  • Bhattacharya,Rabi
  • Majumdar,Mukul
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    Abstract

    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.

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    Bibliographic Info

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    This book is provided by Cambridge University Press in its series Cambridge Books with number 9780521825658 and published in 2007.

    Order: http://www.cambridge.org/uk/catalogue/catalogue.asp?isbn=9780521825658
    Handle: RePEc:cup:cbooks:9780521825658

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    Web page: http://www.cambridge.org

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    Cited by:
    1. Yiyong CAI & Takashi Kamihigashi & John Stachurski, 2013. "Stochastic Optimal Growth with Risky Labor Supply," Discussion Paper Series DP2013-23, Research Institute for Economics & Business Administration, Kobe University.
    2. Majumdar, Mukul, 2009. "Equilibrium and optimality: Some imprints of David Gale," Games and Economic Behavior, Elsevier, vol. 66(2), pages 607-626, July.
    3. Takashi Kamihigashi & John Stachurski, 2011. "An Order-Theoretic Mixing Condition for Monotone Markov Chains," Discussion Paper Series DP2011-24, Research Institute for Economics & Business Administration, Kobe University, revised Sep 2011.
    4. Rabi Bhattacharya & Mukul Majumdar, 2010. "Random iterates of monotone maps," Review of Economic Design, Springer, vol. 14(1), pages 185-192, March.
    5. Guido Cozzi & Fabio Privileggi, 2009. "The fractal nature of inequality in a fast growing world: new version," Working Papers 2009_30, Business School - Economics, University of Glasgow.

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