We study the existence and uniqueness of solution for stochastic differential equations with distributional drift by giving a meaning to the Stroock–Varadhan martingale problem associated to such equations. The approach we exploit is the one of paracontrolled distributions introduced in (Forum Math. Pi 3 (2015) e6). As a result, we make sense of the three-dimensional polymer measure with white noise potential.
"Multidimensional SDEs with singular drift and universal construction of the polymer measure with white noise potential." Ann. Probab. 46 (3) 1710 - 1763, May 2018. https://doi.org/10.1214/17-AOP1213