完全马氏场的存在性、吸引规范及排斥规范

EXISTENCE ABOUT COMPLETE MARKOV RANDOM FIELDS, ATTRACTIVE AND REPULSIVE MARKOV SPECIFICATIONS

在本文中,我们讨论了正则树上一般状态的各向同性完全马氏场的存在性,研究了当马氏规范素∏^((m×φ))是吸引或排斥时M(∏^((m×φ)))的结构。 除特别说明外,文中出现的概念、符号的意义同[6].

LetG(A,～)be a d-dimensional regular tree, X be a polish space, ∏^(m×φ) be a homogeneous Markov specification associated with the state space X and the parameter space A. Let M(∏^(m×φ)) be the set of correspondig Markov random fields, M_o^o(∏^(m×φ)) be the set of corresponding homogeneous complete Markov random fields. We show that if ∏^(m×φ) satisfies a 'boundedness' condition then M_o^o(∏^(m×φ))≠φ. We further study the structure of M(∏^(m×φ)) when ∏^(m×φ) is either attractive or repulsive with respect to a linear ordering on X.