On a Conjecture of an Invariance Principle for Sequences of Associated Random Variables

【摘要】 <正>A finite collection of random variables, X1} —, Xm, is said to be associated if any two coordinatewise nondecreasing functions /i and /a on Rm such that Jt = fj(_Xi} , Xm~) has finite variance for j = l, 2, Oov(/i, _fa)>0; an infinite collection is said to be associated if every finite subcollection is. associated. Thus the concept of "association" is introduced as dependence in probability (Esary, Proschan and Walkup (1967)). It is relative to a lot of practical models, such as the percolation models, the Ising models of statistical mechanics. Therefore, some people are更多还原