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September 2017 Stochastic De Giorgi iteration and regularity of stochastic partial differential equations
Elton P. Hsu, Yu Wang, Zhenan Wang
Ann. Probab. 45(5): 2855-2866 (September 2017). DOI: 10.1214/16-AOP1126

Abstract

Under general conditions, we devise a stochastic version of De Giorgi iteration scheme for semilinear stochastic parabolic partial differential equation of the form

\[\partial_{t}u=\operatorname{div}(A\nabla u)+f(t,x,u)+g_{i}(t,x,u)\dot{w}^{i}_{t}\] with progressively measurable diffusion coefficients. We use the scheme to show that the solution of the equation is almost surely Hölder continuous in both space and time variables.

Citation

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Elton P. Hsu. Yu Wang. Zhenan Wang. "Stochastic De Giorgi iteration and regularity of stochastic partial differential equations." Ann. Probab. 45 (5) 2855 - 2866, September 2017. https://doi.org/10.1214/16-AOP1126

Information

Received: 1 August 2015; Revised: 1 May 2016; Published: September 2017
First available in Project Euclid: 23 September 2017

zbMATH: 06812195
MathSciNet: MR3706733
Digital Object Identifier: 10.1214/16-AOP1126

Subjects:
Primary: 60H15

Keywords: measurable coefficients , Stochastic De Giorgi iteration

Rights: Copyright © 2017 Institute of Mathematical Statistics

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Vol.45 • No. 5 • September 2017
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