Asymptotic behaviour of the cross-variation of some integral long memory processes

Ivan Nourdin (1) , Rola Zintout (2)

1 Probabilités et statistiques
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 $H>\frac12$. 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.

Domaines: Probabilités [math.PR]

Ivan Nourdin, Rola Zintout. Asymptotic behaviour of the cross-variation of some integral long memory processes. 2014. ⟨hal-00903338v2⟩