Asymptotics of locally interacting Markov chains with global signals

Ulrich Horst

No 2001,29, SFB 373 Discussion Papers from Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes

Abstract: We study the long run behaviour of interactive Markov chains on infinite product spaces. The behaviour at a single site is influenced by the local situation in some neighborhood and by a random signal about the average situation throughout the whole system. The asymptotic behaviour 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. Combining a convergence result from the theory of random systems with complete connections with a perturbation of the Dobrushin-Vasserstein contraction technique we show that macroscopic convergence implies that the underlying Microscopic process has local asymptotic loss of memory.

Keywords: Markov chains on infinite product spaces; contraction techniques; Gibbs measures; local asymptotic loss of memory (search for similar items in EconPapers)
Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:zbw:sfb373:200129

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