A Haussmann-Clark-Ocone formula for functionals of diffusion processes with Lipschitz coefficients (Q1394562)

The authors obtain an integral representation (with respect to Brownian motion) for a class of functionals of the diffusion process solution to the stochastic differential equation \[ dX_t= b(t, X_t) dt+ \sigma(t, X_t) dW_t \] with Lipschitz coefficients \(b\) and \(\sigma\). The usual assumption in this kind of problems is the differentiability of the coefficients \(b\) and \(\sigma\). Using generalized derivatives of the coefficients, the authors obtain the integral representation in the nondegenerate case and in the degenerate case. In this last case they also use the Malliavin calculus.