Zhang, Xicheng Stochastic homeomorphism flows of SDEs with singular drifts and Sobolev diffusion coefficients. (English) Zbl 1225.60099 Electron. J. Probab. 16, Paper No. 38, 1096-1116 (2011). Summary: We prove the stochastic homeomorphism flow property and the strong Feller property for stochastic differential equations with sigular time dependent drifts and Sobolev diffusion coefficients. Moreover, the local well-posedness under local assumptions is also obtained. In particular, we extend N. V. Krylov and M. Röckner’s results in [Probab. Theory Relat. Fields 131, No. 2, 154–196 (2005; Zbl 1072.60050)] to the case of non-constant diffusion coefficients. Cited in 1 ReviewCited in 69 Documents MSC: 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) Keywords:stochastic homeomorphism flow; strong Feller property; singular drift; Krylov’s estimates; Zvonkin’s transformation Citations:Zbl 1072.60050 PDFBibTeX XMLCite \textit{X. Zhang}, Electron. J. Probab. 16, Paper No. 38, 1096--1116 (2011; Zbl 1225.60099) Full Text: DOI arXiv EMIS