Quasi sure analysis and Stratonovich anticipative stochastic differential equations (Q1326334)

Consider a stochastic differential equation on \(\mathbb{R}^ d\) with smooth and bounded coefficients. We apply the techniques of the quasi-sure analysis to show that this equation can be solved pathwise out of a slim set. Furthermore, we can restrict the equation to the level sets of a nondegenerate and smooth random variable, and this provides a method to construct the solution to an anticipating stochastic differential equation with smooth and nondegenerate initial condition.