关于加权不变原理的一个注记

在这个注记中我们将关于平稳过程的Davydov弱不变原理推广到长记忆无穷滑动平均过程的加权部分和过程,文中还给出了一些不限于滑动平均过程的一般长记忆时间序列的加权部分和过程增量的二阶矩的边界,这些边界将有助于证明这些过程关于一致度量的胎紧性.作为连续映射定理的一个结果, 我们也导出了一些随机变量函数的概率边界.

A Note on Weighted Invariance Principle

In this note we generalize Davydov's\ucite{1}weak invariance principle for stationary processes to a weightedpartial sums of long memory infinite moving average processes. Thisnote also contains some bounds on the second moments of incrementsof some weighted partial sum processes of a general long memory timeseries, not necessarily moving average type. These bounds are usefulin proving the tightness in uniform metric of these processes. As aconsequence of continuous mapping theorem, the probability bounds oncertain functions of random variables can be established.