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Convergence of locally and globally interacting Markov chains

  • Föllmer, Hans
  • Horst, Ulrich

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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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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  1. William A. Brock & Cars H. Hommes, 1997. "A Rational Route to Randomness," Econometrica, Econometric Society, vol. 65(5), pages 1059-1096, September.
  2. 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.
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