Sobolev differentiable flows of SDEs with local Sobolev and super-linear growth coefficients
Probability
2015-11-25 v3
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 of the associated diffusion semigroup.
Keywords
Cite
@article{arxiv.1407.5834,
title = {Sobolev differentiable flows of SDEs with local Sobolev and super-linear growth coefficients},
author = {Longjie Xie and Xicheng Zhang},
journal= {arXiv preprint arXiv:1407.5834},
year = {2015}
}
Comments
to appear in Annals of Probability