Bounded, attractive and repulsive Markov specifications on trees and on the one-dimensional lattice

Stan Zachary

Stochastic Processes and their Applications, 1985, vol. 20, issue 2, 247-256

Abstract: Let [Pi] be a homogenous Markov specification associated with a countable state space S and countably infinite parameter space A possessing a neighbor relation [small tilde] such that (A,[small tilde]) is the regular tree with d +1 edges meeting at each vertex. Let ([pi])be the simplex of corresponding Markov random fields. We show that if [Pi] satisfies a 'boundedness' condition then ([pi]).We further study the structure of ([pi]) when [Pi] is either attractive or repulsive with respect to a linear ordering on S. When d = 1, so that (A, [small tilde]) is the one-dimensional lattice, we relax the requirement of homogeneity to that of stationarity; here we give sufficient conditions for ([pi]) and for ([pi])to have precisely one member.

Keywords: phase; transition; Markov; random; fields; Markov; chains; on; infinite; trees; attractive; specifications; repulsive; specifications (search for similar items in EconPapers)
Date: 1985
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0304-4149(85)90213-3
Full text for ScienceDirect subscribers only

Related works:
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:20:y:1985:i:2:p:247-256

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 ().