随机场重对数律的一种精确渐近性

One precise asymptotics in the law of the iterated logarithm of random fields.

讨论了随机场重对数律精确渐近性的一种形式,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,EX2=2σ<∞,则li mε0ε2∑n1|n|(log|n|)dP(|Sn|≥ε|n|loglog|n|)=(d-σ21)!.

One orecise asymptotics is obtained in the law of the iterated logarithm of random fields, let {X,Xk,k∈Z＋^d,x（i）,i≥1}be the i. i. d random variables, and EX=0,EX^2=σ^2〈∞, the result is proved as follows. limc→0ε^2∑n 1/｜n｜（log｜n｜）^dP（｜Sn｜≥ε√｜n｜loglog｜n｜）=σ^2/（d-1）!