A change of variable formula for the 2D fractional Brownian motion of Hurst index bigger or equal to 1/4

Ivan Nourdin (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

We prove a change of variable formula for the 2D fractional Brownian motion of index H bigger of equal to 1/4. For H strictly bigger than 1/4, our formula coincides with that obtained by using the rough paths theory. For H=1/4 (the more interesting case), there is an additional term that is a classical Wiener integral against an independent standard Brownian motion.

Mots clés: Fractional Brownian motion; weak convergence; change of variable formula

Domaines: Probabilités [math.PR]

Ivan Nourdin. A change of variable formula for the 2D fractional Brownian motion of Hurst index bigger or equal to 1/4. 2008. ⟨hal-00287990v2⟩