Convergence of weighted sums of random variables with long-range dependence

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• 作者：Pipiras ; Vladas ; Taqqu ; Murad S.
• 关键词：60F05 ; 60G18 ; 60H05 ; 42A38 ; Weierstrass&ndash ; Mandelbrot process ; Fractional Brownian motion ; Long-range dependence ; Integral with respect to fractional Brownian motion ; Time and spectral domains ; Fourier transform
• 刊名：Stochastic Processes and their Applications
• 出版年：2000
• 出版时间：November, 2000
• 年：2000
• 卷：90
• 期：1
• 页码：157-174
• 全文大小：170 K

文摘

Suppose that Cannot display formula . We also consider two examples. In contrast to the case when the ξ_n'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′−.