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Convergence of locally and globally interacting Markov chains

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Author Info

  • Föllmer, Hans
  • Horst, Ulrich

Abstract

We study the long run behaviour of interactive Markov chains on infinite product spaces. In view of microstructure models of financial markets, the interaction has both a local and a global component. The convergence of such Markov chains is analyzed on the microscopic level and on the macroscopic level of empirical fields. We give sufficient conditions for convergence on the macroscopic level. Using a perturbation of the Dobrushin-Vasserstein contraction technique we show that macroscopic convergence implies weak convergence of the underlying Markov chain. This extends the basic convergence theorem of Vasserstein for locally interacting Markov chains to the case where an additional global component appears in the interaction.

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Bibliographic Info

Article provided by Elsevier in its journal Stochastic Processes and their Applications.

Volume (Year): 96 (2001)
Issue (Month): 1 (November)
Pages: 99-121

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Handle: RePEc:eee:spapps:v:96:y:2001:i:1:p:99-121

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Related research

Keywords: Markov chains on infinite product spaces Convergence of Markov chains Contraction techniques Gibbs measures;

References

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  1. Horst, Ulrich, 2001. "Asymptotics of locally interacting Markov chains with global signals," SFB 373 Discussion Papers 2001,29, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  2. repec:wop:humbsf:2001-29 is not listed on IDEAS
  3. William A. Brock & Cars H. Hommes, 1997. "A Rational Route to Randomness," Econometrica, Econometric Society, vol. 65(5), pages 1059-1096, September.
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Cited by:
  1. Alberto Bisin & Andrea Moro & Giorgio Topa, 2011. "The Empirical Content of Models with Multiple Equilibria in Economies with Social Interactions," NBER Working Papers 17196, National Bureau of Economic Research, Inc.
  2. ÖZGÜR, Onur & BISIN, Alberto, 2011. "Dynamic Linear Economies with Social Interactions," Cahiers de recherche 04-2011, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  3. Ulrich Horst & Jos´e A. Scheinkman, 2006. "A Limit Theorem for Systems of Social Interactions," Levine's Bibliography 321307000000000177, UCLA Department of Economics.
  4. Biao Wu, 2007. "Interacting Agent Feedback Finance Model," Papers math/0703827, arXiv.org.
  5. U. Horst & Jose A. Scheinkman, 2010. "Equilibria in Systems of Social Interactions," Levine's Working Paper Archive 506439000000000119, David K. Levine.
  6. Onur Ozgur & Alberto Bisin, 2011. "Dynamic linear economies with social interactions," Levine's Working Paper Archive 786969000000000036, David K. Levine.
  7. Alberto Bisin & Thierry Verdier, 2010. "The Economics of Cultural Transmission and Socialization," NBER Working Papers 16512, National Bureau of Economic Research, Inc.

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