@article{cfb4cfdb84c74ba5a05c9f5a4af01c6a,
title = "Sobolev differentiable flows of SDEs with local Sobolev and super-linear growth coefficients",
abstract = "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.",
keywords = "Irreducibility, Krylov's estimate, Strong Feller property, Weak differentiability, Zvonkin's transformation",
author = "Longjie Xie and Xicheng Zhang",
note = "Publisher Copyright: {\textcopyright} Institute of Mathematical Statistics, 2016.",
year = "2016",
doi = "10.1214/15-AOP1057",
language = "English",
volume = "44",
pages = "3661--3687",
journal = "Annals of Probability",
issn = "0091-1798",
publisher = "Institute of Mathematical Statistics",
number = "6",
}