随机场下重对数律的渐近性  

ASYMPTOTICS IN THE LAWS OF THE ITERATED LOGARITHM FOR RANDOM FIELDS

作　　者：牛司丽[1] 

机构地区：[1]同济大学应用数学系,上海200092

出　　处：《数学年刊（A辑）》2004年第4期415-424,共10页Chinese Annals of Mathematics

摘　　要：设{X,X_k,k∈z_+~d)是d维随机场独立同分布零均值的随机变量,如果E[X^2(log^+|X|)^(α+d-1)(log+log^+|X|)~β]<∞,则 其中Γ(·)为Gamma函数.由此回答了Gut和Spataru[4]在d=1时所提出的问题。Consider Z_+~d (d≥2) the positive integer d-dimensional lattice points with partial ordering ≤, let {X, X_k, k ∈Z_+~d} be i.i.d, random variables with mean 0, and set S_n= X_k. It is proves that for α>-1, β>-1/2, whenever EX^2 =σ~2, E[X^2(log^+|X|)^(a+d-1)(log^+log^+|X|)~β]<∞, where Γ(·) is a gamma function. This result answers the question mentioned by Gut and Spataru [4] in the case d=1.

关 键 词：随机场 独立随机变量 重对数律 渐近性 

分 类 号：O211.6[理学—概率论与数理统计]