Weak approximation of a fractional SDE

Xavier Bardina, Ivan Nourdin, Carles Rovira and Samy Tindel

Departament de Matemàtiques, Facultat de Ciències, Edifici C, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain.
Laboratoire de Probabilités et Modèles Aléatoires, Université Pierre et Marie Curie, Boîte courrier 188, 4 Place Jussieu, 75252 Paris Cedex 5, France.
Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain.
Institut Élie Cartan Nancy, B.P. 239, 54506 Vandoeuvre-lès-Nancy Cedex, France.

Abstract

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, and our method of proof relies on the algebraic integration theory introduced by Gubinelli.

Published in: Stochastic Processes and their Applications, 120 (1), 39-65, 2010.