Xie, Longjie; Zhang, Xicheng Sobolev differentiable flows of SDEs with local Sobolev and super-linear growth coefficients. (English) Zbl 1405.60081 Ann. Probab. 44, No. 6, 3661-3687 (2016). The authors establish a characterization for Sobolev differentiability of random fields. They use their characterization to prove weak differentiability of solutions to stochastic differential equations with local Sobolev and super-linear growth coefficients, with respect to the starting point. They go on to study the strong Feller property and the irreducibility of the associated diffusion semigroup. Reviewer: Denis R. Bell (Jacksonville) Cited in 20 Documents MSC: 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) 60J60 Diffusion processes Keywords:weak differentiability; Krylov’s estimate; Zvonkin’s transformation; strong Feller differentiability; irreducibility PDFBibTeX XMLCite \textit{L. Xie} and \textit{X. Zhang}, Ann. Probab. 44, No. 6, 3661--3687 (2016; Zbl 1405.60081) Full Text: DOI arXiv