One of the most useful results from Malliavin calculus is the Clark-Ocone theorem, which allows the process in the martingale representation theorem to be identified explicitly.
For F: C[0,1] \to \R satisfying E(F(X)^2) < \infty which is Lipschitz and such that F has a strong derivative kernel, in the sense that for \varphi in C[0,1] .