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November 2016 Sobolev differentiable flows of SDEs with local Sobolev and super-linear growth coefficients
Longjie Xie, Xicheng Zhang
Ann. Probab. 44(6): 3661-3687 (November 2016). DOI: 10.1214/15-AOP1057

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.

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Longjie Xie. Xicheng Zhang. "Sobolev differentiable flows of SDEs with local Sobolev and super-linear growth coefficients." Ann. Probab. 44 (6) 3661 - 3687, November 2016. https://doi.org/10.1214/15-AOP1057

Information

Received: 1 April 2015; Revised: 1 August 2015; Published: November 2016
First available in Project Euclid: 14 November 2016

zbMATH: 06674835
MathSciNet: MR3572321
Digital Object Identifier: 10.1214/15-AOP1057

Subjects:
Primary: 60H10, 60J60

Rights: Copyright © 2016 Institute of Mathematical Statistics

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Vol.44 • No. 6 • November 2016
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