Convergence of locally and globally interacting Markov chains

Hans Föllmer and Ulrich Horst

Stochastic Processes and their Applications, 2001, vol. 96, issue 1, 99-121

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.

Keywords: Markov; chains; on; infinite; product; spaces; Convergence; of; Markov; chains; Contraction; techniques; Gibbs; measures (search for similar items in EconPapers)
Date: 2001
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (18)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304-4149(01)00110-7
Full text for ScienceDirect subscribers only

Related works:
Working Paper: Convergence of locally and globally interacting Markov chains (2001)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:96:y:2001:i:1:p:99-121

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().