## Annals of Probability

### 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.

#### Article information

Source
Ann. Probab., Volume 44, Number 6 (2016), 3661-3687.

Dates
Revised: August 2015
First available in Project Euclid: 14 November 2016

Permanent link to this document
https://projecteuclid.org/euclid.aop/1479114260

Digital Object Identifier
doi:10.1214/15-AOP1057

Mathematical Reviews number (MathSciNet)
MR3572321

Zentralblatt MATH identifier
06674835

#### Citation

Xie, Longjie; Zhang, Xicheng. Sobolev differentiable flows of SDEs with local Sobolev and super-linear growth coefficients. Ann. Probab. 44 (2016), no. 6, 3661--3687. doi:10.1214/15-AOP1057. https://projecteuclid.org/euclid.aop/1479114260

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