Convergence of locally and globally interacting Markov chains
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.
Volume (Year): 96 (2001)
Issue (Month): 1 (November)
|Contact details of provider:|| Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description|
|Order Information:|| Postal: http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional|
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Brock, W.A., 1995.
"A Rational Route to Randomness,"
9530, Wisconsin Madison - Social Systems.
- 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.
When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:96:y:2001:i:1:p:99-121. See general information about how to correct material in RePEc.
If references are entirely missing, you can add them using this form.