关于修整和强逼近的一个注记

摘要

Let {X, Xn; n >1} be a sequence of independent and identically distributed random variables, and let Xn(r) = Xm if |Xm| is the r-th maximum of {|Xk|; k≤n}.Define Sn = ∑k≤n Xk and (r)Sn = Sn- (Xn(1) +···+Xn(r)).This paper aims to establish a general strong approximation for the trimmed sums (r)Sn without variance, and as applications, general functional laws of the iterated logarithm for trimmed sums and products of trimmed sums are derived.%设{X,Xn；n≥1｝是一独立同分布的随机变量序列.如果｜Xm｜是新序列{｜Xκ｜；κ≤ n｝中的第r大元素,则令X(r)n=Xm.同时记部分和与修整和分别为Sn=n∑κ=1 Xκ和(r)Sn=Sn-(X(1)n+…+X(r)n)).该文在EX2可能是无穷的条件下,得到了修整和(r)Sn的广义强逼近定理.作为应用,建立了关于修整和以及修整和乘积的广义泛函重对数律.