随机场重对数律的精确渐近性

Precise asymptotics in the law of the iterated logarithm of random fields.

设{ X ,Xk,k∈Zd + ,X (i) ,i≥1}是独立同分布的随机变量序列,且EX =0 ,对δ>0 ,E X2 (log log|X |) 1 +δ<∞.令Sn =∑k≤nXk。

Let \${X,X\-k,k∈Z\+d\++,X(i),i≥1}\$ be i.i.d random variables sequence. And \$EX=0, S\-n=∑k≤nX\-k\$, the following result is proved \$\{\%lim\%\}εσ2ε\+2-2σ\+2∑n\%log\%|n|\+\{-(d-1)\}|n|P|S\-n|≥ε|n|\%log log\%|n|=σ2(d-1)!.\$ Whenever \$EX\+2(\%log log\%|X|)\+\{1+δ\}]