Cross-variation of Young integral with respect to long-memory fractional Brownian motions35
Słowa kluczowe:
Fractional Brownian motion, Rosenblatt process, Young integral, Breuer–Major theorem, Taqqu’s theorem, stochastic differential equationsAbstrakt
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.
