  We consider anticipative Stratonovich stochastic differential equations
driven by some stochastic process (not necessarily a semi-martingale). No
adaptedness of initial point or vector fields is assumed. Under a simple
condition on the stochastic process, we show that the unique solution of the
above SDE understood in the rough path sense is actually a Stratonovich
solution. This condition is satisfied by the Brownian motion and the fractional
Brownian motion with Hurst parameter greater than 1/4. As application, we
obtain rather flexible results such as support theorems, large deviation
principles and Wong-Zakai approximations for SDEs driven by fractional Brownian
Motion along anticipating vectorfields. In particular, this unifies many
results on anticipative SDEs.
