“转移律、马氏规范及马氏场”一文的几点注记

SEVERAL REMARKS ON “TRANSITIONAL LAWS, MARKOV SPACIFICATIONS AND MARKOV RANDOM FIELDS”

在[3]中,作者对树上一般状态的马氏场证明了在一定条件下完全马氏场与转移律之间存在一一对应关系,并且利用此结果证明了正则树上有限状态各向同性完全马氏场的存在性。本文的目的有如下几个:首先说明用与[3]中证明定理2.3相同的方法可把定理2.3推广到X是紧Polish空间且φ连续的情形。

In this paper, We discuss the general state space Markov random fields on d-dimensional regular trees. First of all,We show an existence theorem about homogeneous complete Markov random fields with a compact Polish state space, and then We discuss relation between complete Markov random fields and Markov processes and give a sufficent condition for M_o^o=M_o^1,=M^o When d=1.