[hal-00903338] Asymptotic behaviour of the cross-variation of some integral long memory processes

We study the asymptotic behaviour of the cross-variation of two-dimensional processes having the form of a Young integral with respect to a fractional Brownian motion of index $H\frac12$ When $H$ is smaller than or equal to 3/4 we show asymptotic mixed normality When $H$ is stricly bigger than 3/4 we obtain a limit that is expressed in terms of the difference of two independent Rosenblatt processes



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