Regularization of differential equations by fractional noise

Let {BtH,t∈[0,T]} be a fractional Brownian motion with Hurst parameter H. We prove the existence and uniqueness of a strong solution for a stochastic differential equation of the form Xt=x+BtH+∫0tb(s,Xs) ds, where b(s,x) is a bounded Borel function with linear growth in x (case H⩽12) or a Hölder continuous function of order strictly larger than 1−1/2H in x and than H−12 in time (case H>12).