Xie, Longjie et Zhang, Xicheng, Sobolev differentiable flows of SDEs with local Sobolev and super-linear growth coefficients, Annals of probability , 44(6), 2016, pp. 3661-3687
By establishing a characterization for Sobolev differentiability of random fields, we prove the weak differentiability of solutions to stochastic differential equations with local Sobolev and super-linear growth coefficients with respect to the starting point. Moreover, we also study the strong Feller property and the irreducibility to the associated diffusion semigroup.