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

Vladas Pipiras and Murad S. Taqqu

Stochastic Processes and their Applications, 2000, vol. 90, issue 1, 157-174

Abstract: Suppose that f is a deterministic function, is a sequence of random variables with long-range dependence and BH is a fractional Brownian motion (fBm) with index . In this work, we provide sufficient conditions for the convergencein distribution, as m-->[infinity]. We also consider two examples. In contrast to the case when the [xi]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 .

Keywords: Weierstrass-Mandelbrot; process; Fractional; Brownian; motion; Long-range; dependence; Integral; with; respect; to; fractional; Brownian; motion; Time; and; spectral; domains; Fourier; transform (search for similar items in EconPapers)
Date: 2000
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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