“…Recently, there are increasing interests to extend the classical DiPerna-Lions theory [7] about ordinary differential equations (ODE) with Sobolev coefficients to the case of stochastic differential equations (SDE) (cf. [14,15,10,26,27,28,9,16]). In [10], Figalli first extended the DiPerna-Lions theory to SDE in the sense of martingale solutions by using analytic tools and solving deterministic Fokker-Planck equations.…”