Stochastic differentiation - A generalized approach

The space (D*) of Wiener distributions allows a natural Pettis-type stochas tic calculus. For a certain class of generalized multiparameter processes X : R-N--> (D*) we prove several differentiation rules (Ito formulas); these processes can be anticipating. We then apply these rules to some examples o f square integrable Wiener functionals and look at the integral versions of the resulting formulas.