  In this paper, we study the existence and uniqueness of a class of stochastic
differential equations driven by fractional Brownian motions with arbitrary
Hurst parameter $H\in (0,1)$. In particular, the stochastic integrals appearing
in the equations are defined in the Skorokhod sense on fractional Wiener
spaces, and the coefficients are allowed to be random and even anticipating.
The main technique used in this work is an adaptation of the anticipating
Girsanov transformation of Buckdahn [Mem. Amer. Math. Soc. 111 (1994)] for the
Brownian motion case. By extending a fundamental theorem of Kusuoka [J. Fac.
Sci. Univ. Tokyo Sect. IA Math. 29 (1982) 567--597] using fractional calculus,
we are able to prove that the anticipating Girsanov transformation holds for
the fractional Brownian motion case as well. We then use this result to prove
the well-posedness of the SDE.
