Countable State Space Markov Random Fields and Markov Chains on Trees

Abstract

896 STAN ZACHARY Theorem 2.1. Let the Markov random field P on (SA, ¡F) have trivial tail a-field. Then P is a Markov chain. Proof. We must show that for each V e тГ *, W С V, xw e Sw, (2.2) Р{Ы= xw/nV\W)} = P{tw=xw/nVndW)}. Consider any U e "V such that V С U. We ...