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We consider anticipative Stratonovich stochastic differential equationsdriven by some stochastic process lifted to a rough path. Neither adaptednessof initial point and vector fields nor commuting conditions between vectorfield is assumed. Under a simple condition on the stochastic process, we showthat the unique solution of the above SDE understood in the rough path sense isactually a Stratonovich solution. We then show that this condition is satisfiedby the Brownian motion. As application, we obtain rather flexible results suchas support theorems, large deviation principles and Wong--Zakai approximationsfor SDEs driven by Brownian motion along anticipating vectorfields. Inparticular, this unifies many results on anticipative SDEs.

Good rough path sequences and applications to anticipating stochastic calculus