Stochastic differential equations for fractional Brownian motions

We construct via dyadic approximations a canonical geometric rough path in the sense of [7] associated to a fractional Brownian motion with Hurst parameter h, h epsilon]1/4, 1/2[. Therefore, we obtain a Wong-Zakai type approximation theorem for solutions of stochastic differential equations driven by these fractional Brownian motions. (C) 2000 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.