We study the weak differentiability of global strong solution of stochastic differential equations, the strong Feller property of the associated diffusion semigroups and the global stochastic flow property in which the singular drift term and the weak gradient of Sobolev diffusion term are supposed to satisfy local growth conditions respectively. The main tools for these results are the decomposition of global two-point motions, Krylov's estimate, Khasminskii's estimate, Zvonkin's transformation and the characterization for Sobolev differentiability of random fields.
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