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Cross-variation of Young integral with respect to long-memory fractional Brownian motions

Nourdin I., Zintout R.

Probability and Mathematical Statistics

2016

Vol. 36, Fasc. 1

35--46

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 > 1/2 . When H is smaller than or equal to 3/4 , we show asymptotic mixed normality. When H is stricly greater than 3/4 , we obtain a limit that is expressed in terms of the difference of two independent Rosenblatt processes.