相伴随机场的Berry-Esseen不等式和不变原理

A BERRY-ESSEEN INEQUALITY AND AN INVARIANCE PRINCIPLE FOR ASSOCIATED RANDOM FIELDS

本文在较一般的条件下讨论了相伴随机场的 Berry-Esseen 不等式和不变原理,并对相伴随机变量序列得到了 n^(-1/4)的 Berry-Esseen 阶,改进了 Wood(1983),Newman-Wright,Cox-Grimmett等人的结论.

In this paper we establish a Berry-Esseen inequality and an invariance prinoipe for associated random fields{X_n(N),n∈A(K(N))}under the assumptions i)EX(_n^2)(N)≥c>0 and EX_n(N)=0 for every n,N ii) where{K(N)}is a sequence in z^d with ‖A(K(N))‖→∞. iii)Coy(X_j(N),X_n(N))≤u(r)for r≥0 where u(r)→0 as r→∞ The results obtained improve the theorem of Cox and Grimment(1984).