Weak approximation of a fractional SDE

Ivan Nourdin (1) , Samy Tindel (2)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 IECN - Institut Élie Cartan de Nancy

In this note, a diffusion approximation result is shown for stochastic differential equations driven by a fractional Brownian motion B with Hurst parameter H>1/3. We shall use a Gaussian regular approximation of B for sake of clarity, and our method of proof will rely on the algebraic integration theory introduced by Gubinelli.

Mots clés: Weak approximation; fractional Brownian motion; rough paths

Domaines: Probabilités [math.PR]

Ivan Nourdin, Samy Tindel. Weak approximation of a fractional SDE. 2007. ⟨hal-00170074v1⟩