Quadratic Covariation and Itos Formula for Smooth Nondegenerate Martingales

In this paper we prove the existence of the quadratic covariation [f(X),X], where f is a locally square integrable function and X t = (integral) t 0 u s dW s is a smooth nondegenerate Brownian martingale. This result is based on some moment estimates for Riemann sums which are established by means of the techniques of the Malliavin calculus.