Weak approximation of a fractional SDE

Xavier Bardina (1) , Ivan Nourdin (2) , Carles Rovira (3) , Samy Tindel (4, 5)

1 UAB - Departament de Matemàtiques [Barcelona]
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
3 Facultat de Matematiques
4 IECN - Institut Élie Cartan de Nancy
5 BIGS - Biology, genetics and statistics

In this note, a diffusion approximation result is shown for stochastic differential equations driven by a (Liouville) fractional Brownian motion B with Hurst parameter H in (1/3,1/2). More precisely, we resort to the Kac-Stroock type approximation using a Poisson process studied in Bardina, Jolis and Tudor (2003) and Delgado and Jolis (2000), and our method of proof relies on the algebraic integration theory introduced by Gubinelli (2004).

Mots clés: Weak approximation; Kac-Stroock type approximation; fractional Brownian motion; rough paths; Weak approximation

Domaines: Probabilités [math.PR]

Xavier Bardina, Ivan Nourdin, Carles Rovira, Samy Tindel. Weak approximation of a fractional SDE. Stochastic Processes and their Applications, 2010, 120 (1), pp.39-65. ⟨10.1016/j.spa.2009.10.008⟩. ⟨hal-00170074v2⟩