Strong solutions of SDE's with rough coefficients

Abstract

We give a proof of the strong existence and the regularity of stochastic differential equations driven by a Brownian motion and a measurable, Markovian drift without no regularity hypothesis except that the Girsanov exponential associated is in some L^{1+ε}(μ) for some fixed ε>0 by using the techniques which are totally novel originating from the abstract Wiener space, in particular the solution is an H-C-regular map in the sense of the theory of Leonard Gross.

Some typos corrected and notations better explained