Convergence of weighted sums of random variables with long-range dependence (
Convergence of weighted sums of random variables with long-range dependence (
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具有长程依赖性的随机变量加权和的收敛性（
DOI：
10.1016/s0304-4149(00)00040-5
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发表时间：
2000
期刊：
影响因子：
--
通讯作者：
M. Taqqu
中科院分区：
文献类型：
--
作者：
V. Pipiras;M. Taqqu
设f是确定性函数，{n}n∈ Z是长程相依随机变量序列，BHis是指数H∈（12，1）的分数布朗运动（fBm）.在这项工作中，我们提供了当m→∞时分布收敛的充分条件[公式：见正文]。我们还考虑两个例子。与双列直插的情况相反。在有限方差下，如果f是Weierstrass-Mandelbrot过程的核，则极限不是fBm。然而，如果f是来自指标为H′的fBm的“移动平均”表示的核函数，则极限是指标为H+H′− 1 2的fBm。
Suppose that f is a deterministic function, {ξn}n∈Zis a sequence of random variables with long-range dependence and BHis a fractional Brownian motion (fBm) with index H∈( 1 2 ,1) . In this work, we provide sufficient conditions for the convergence [Formula: see text] in distribution, as m→∞. We also consider two examples. In contrast to the case when the ξn's are i.i.d. with finite variance, the limit is not fBm if f is the kernel of the Weierstrass–Mandelbrot process. If however, f is the kernel function from the “moving average” representation of a fBm with index H′, then the limit is a fBm with index H+H′− 1 2 .