Equation différentielle anticipative sur une variété et approximations Original Research Article

This paper is the sequel of a paper by the authors (1993) and it has a complete version in (1995). We develop a stochastic calculus which allows to integrate non-adapted processes taking their values in the space of second-order 1-forms that are above a manifold valued anticipating process. Using that integration, we study the existence and uniqueness of solution of an anticipating stochastic differential equation in a manifold. This stochastic calculus uses both second-order geometry defined by P.-A. Meyer (1981) and Nualart-Pardouxʹs duality definition of Skorohod integral (1988).