×

Sobolev differentiable flows of SDEs with local Sobolev and super-linear growth coefficients. (English) Zbl 1405.60081

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.

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60J60 Diffusion processes
PDFBibTeX XMLCite
Full Text: DOI arXiv