Multidimensional SDEs with singular drift and universal construction of the polymer measure with white noise potential

Abstract

We study existence and uniqueness of solution for stochastic differential equations with distributional drift by giving a meaning to the Stroock-Varadhan martingale problem associated such equations. The approach we exploit is the one of paracontrolled distributions introduced in [13]. As a result we make sense of the three dimensional polymer measure with white noise potential.

We improved the presentation, corrected some of the proofs and added the global existence for the polymer measure in dimension 3