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

Ivan Nourdin (1) , Rola Zintout (2)

1 FSTC - Faculté des Sciences, de la Technologie et de la Communication
2 IECL - Institut Élie Cartan de Lorraine

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 strictly bigger than $3/4$, we obtain a limit that is expressed in terms of the difference of two independent Rosenblatt processes.

Domaines: Probabilités [math.PR]

Ivan Nourdin, Rola Zintout. Cross-variation of Young integral with respect to long-memory fractional Brownian motions. 2015. ⟨hal-00903338v3⟩