Anticipating integrals for a class of martingales

Abstract

An anticipating stochastic integral is proposed for 'normal martingales'. It agrees with the Skorohod integral in the Brownian case. A variational derivative of Malliavin type is also defined. An integration by parts formula is given which has some subtle and important differences from the formula in the Brownian case. The existence and uniqueness of solutions of linear stochastic differential equations with anticipating exogenous driving terms are also established.