STOCHASTIC DE GIORGI ITERATION AND REGULARITY OF STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS

被引：7

作者：

Hsu, Elton P. ^{[1
]}

Wang, Yu ^{[2
]}

Wang, Zhenan ^{[3
]}

机构：

[1] Northwestern Univ, Dept Math, Evanston, IL 60521 USA

[2] Goldman Sachs, 20 Rivercourt,Apt 1807, Jersey City, NJ 07310 USA

[3] Univ Washington, Dept Math, Padelford Hall,Off C332, Seattle, WA 98195 USA

来源：

ANNALS OF PROBABILITY | 2017年 / 45卷 / 05期

关键词：

Stochastic De Giorgi iteration; measurable coefficients;

D O I：

10.1214/16-AOP1126

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Under general conditions, we devise a stochastic version of De Giorgi iteration scheme for semilinear stochastic parabolic partial differential equation of the form partial derivative(t)u = div(A del u) + f(t, x, u) + g(i)(t, x, u)<(w)over dot>(i)(t) with progressively measurable diffusion coefficients. We use the scheme to show that the solution of the equation is almost surely Holder continuous in both space and time variables.

引用

页码：2855 / 2866

页数：12