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

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 .