Green formulas in anticipating stochastic calculus

In this paper we state Green type formulas for nonadapted processes with respect to “anticipating semimartingales”, say U, in the Stratonovich and the Skorohod formulation. To this end we develop some notions of anticipating stochastic calculus with respect to U, based on multiple and line integrals. The basic ingredients are a Hu-Meyer formula for multiple integrals with respect to U and a Fubini theorem for the multiple Stratonovich integral.