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

共 17 条

[1]

[Anonymous], 1992, ENCY MATH ITS APPL, DOI DOI 10.1017/CBO9780511666223

[2] Ito's formula in UMD Banach spaces and regularity of solutions of the Zakai equation [J].

Brzezniak, Z. ;

van Neerven, J. M. A. M. ;

Veraar, M. C. ;

Weis, L. .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2008, 245 (01) :30-58

[3] THE DE GIORGI METHOD FOR REGULARITY OF SOLUTIONS OF ELLIPTIC EQUATIONS AND ITS APPLICATIONS TO FLUID DYNAMICS [J].

Caffarelli, Luis A. ;

Vasseur, Alexis F. .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2010, 3 (03) :409-427

[4]

Caffarelli LA, 2010, ANN MATH, V171, P1903

[5]

Carmona Rene A., 1999, Mathematical Surveys and Monographs, V64, DOI [10.1090/surv/064, DOI 10.1090/SURV/064]

[6]

DEBUSSCHE A, ARXIV14016369

[7]

GLATT-HOLTZ G, ARXIV13020542V1

[8]

Krylov NV, 2010, PROBAB THEORY REL, V147, P583, DOI 10.1007/s00440-009-0217-7

[9]

Krylov N.V., 1999, MATH SURVEYS MONOGR, V64, P185

[10] On L(p)-theory of stochastic partial differential equations in the whole space [J].

Krylov, NV .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1996, 27 (02) :313-340

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