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Random Dynamical Systems

Author

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  • Bhattacharya,Rabi
  • Majumdar,Mukul

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.

Suggested Citation

  • Bhattacharya,Rabi & Majumdar,Mukul, 2007. "Random Dynamical Systems," Cambridge Books, Cambridge University Press, number 9780521532723.
  • Handle: RePEc:cup:cbooks:9780521532723
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    Citations

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    Cited by:

    1. Annarita COLASANTE & Antonio PALESTRINI & Alberto RUSSO & Mauro GALLEGATI, 2015. "Adaptive Expectations with Correction Bias: Evidence from the lab," Working Papers 409, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    2. Anna Jaśkiewicz & Janusz Matkowski & Andrzej Nowak, 2014. "On variable discounting in dynamic programming: applications to resource extraction and other economic models," Annals of Operations Research, Springer, vol. 220(1), pages 263-278, September.
    3. Felix KUBLER & Karl SCHMEDDERS, 2010. "Life-Cycle Portfolio Choice, the Wealth Distribution and Asset Prices," Swiss Finance Institute Research Paper Series 10-21, Swiss Finance Institute.
    4. 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.
    5. Çisem Bektur, 2013. "Performance of investment strategies in the absence of correct beliefs," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 36(1), pages 23-37, May.
    6. Anna Jaśkiewicz & Andrzej Nowak, 2011. "Stochastic Games with Unbounded Payoffs: Applications to Robust Control in Economics," Dynamic Games and Applications, Springer, vol. 1(2), pages 253-279, June.
    7. Antonio Palestrini, 2015. "Firm Size Distribution and the Survival Bias," Economics Bulletin, AccessEcon, vol. 35(3), pages 1630-1637.
    8. Cai, Yiyong & Kamihigashi, Takashi & Stachurski, John, 2014. "Stochastic optimal growth with risky labor supply," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 167-176.
    9. repec:eee:jetheo:v:175:y:2018:i:c:p:624-651 is not listed on IDEAS
    10. Kamihigashi, Takashi & Stachurski, John, 2012. "An order-theoretic mixing condition for monotone Markov chains," Statistics & Probability Letters, Elsevier, vol. 82(2), pages 262-267.
    11. Mauro Gaggero & Giorgio Gnecco & Marcello Sanguineti, 2014. "Approximate dynamic programming for stochastic N-stage optimization with application to optimal consumption under uncertainty," Computational Optimization and Applications, Springer, vol. 58(1), pages 31-85, May.
    12. Rabi Bhattacharya & Mukul Majumdar, 2010. "Random iterates of monotone maps," Review of Economic Design, Springer;Society for Economic Design, vol. 14(1), pages 185-192, March.
    13. Thomas, Jonathan P. & Worrall, Tim, 2014. "Dynamic Relational Contracts under Complete Information," 2007 Annual Meeting, July 29-August 1, 2007, Portland, Oregon TN 2015-47, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    14. Thomas, Jonathan P. & Worrall, Tim, 2014. "Dynamic Relational Contracts under Complete Information," SIRE Discussion Papers 2015-47, Scottish Institute for Research in Economics (SIRE).
    15. Majumdar, Mukul, 2009. "Equilibrium and optimality: Some imprints of David Gale," Games and Economic Behavior, Elsevier, vol. 66(2), pages 607-626, July.
    16. Takashi Kamihigashi & John Stachurski, 2014. "Stability Analysis for Random Dynamical Systems in Economics," Discussion Paper Series DP2014-35, Research Institute for Economics & Business Administration, Kobe University.
    17. Bishnu, Monisankar, 2010. "Essays on optimal allocation of resources by governments," ISU General Staff Papers 201001010800002441, Iowa State University, Department of Economics.
    18. Gallegati, M. & Palestrini, A., 2010. "The complex behavior of firms' size dynamics," Journal of Economic Behavior & Organization, Elsevier, vol. 75(1), pages 69-76, July.
    19. Antonio Palestrini & Mauro Gallegati, 2015. "Unbiased Adaptive Expectation Schemes," Economics Bulletin, AccessEcon, vol. 35(2), pages 1185-1190.
    20. John Stachurski, 2009. "Economic Dynamics: Theory and Computation," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262012774, January.

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