Anticipating Stochastic Differential Equations of Stratonovich Type

摘要

We prove the existence and uniqueness of Stratonovich stochastic differential equations where the coefficients and the initial condition may depend on the whole path of the driving Wiener process. Our main hypothesis is that the diffusion coefficient satisfies the Frobenius condition. The solution is given in terms of solutions of ordinary differential equations and the Wiener process. We use this representation to study properties of the solution.