International Journal of Stochastic Analysis
Volume 2012 (2012), Article ID 281474, 13 pages
Research Article

A Stability Result for Stochastic Differential Equations Driven by Fractional Brownian Motions

Laboratoire de Mathématiques de Besançon, UMR CNRS 6623, Université de Franche-Comté, 16 route de Gray, 25030 Besançon, France

Received 26 July 2012; Accepted 7 November 2012

Academic Editor: Agnès Sulem

Copyright © 2012 Bruno Saussereau. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We study the stability of the solutions of stochastic differential equations driven by fractional Brownian motions with Hurst parameter greater than half. We prove that when the initial conditions, the drift, and the diffusion coefficients as well as the fractional Brownian motions converge in a suitable sense, then the sequence of the solutions of the corresponding equations converge in Hölder norm to the solution of a stochastic differential equation. The limit equation is driven by the limit fractional Brownian motion and its coefficients are the limits of the sequence of the coefficients.