Pathwise Numerical Approximations of SPDEs with Additive Noise under Non-global Lipschitz Coefficients

被引：47

作者：

Jentzen, Arnulf ^{[1
]}

机构：

[1] Goethe Univ Frankfurt, Inst Math, D-60325 Frankfurt, Germany

来源：

POTENTIAL ANALYSIS | 2009年 / 31卷 / 04期

关键词：

Parabolic stochastic partial differential equation; Higher order approximation; Strong error criteria; Global Lipschitz; Pathwise approximation; PARTIAL-DIFFERENTIAL-EQUATIONS; NONUNIFORM TIME DISCRETIZATION; IMPLICIT SCHEME; EULER SCHEME; DRIVEN;

D O I：

10.1007/s11118-009-9139-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the pathwise numerical approximation of nonlinear parabolic stochastic partial differential equations (SPDEs) driven by additive white noise under local assumptions on the coefficients only. We avoid the standard global Lipschitz assumption in the literature on the coefficients by first showing convergence under global Lipschitz coefficients but with a strong error criteria and then by applying a localization technique for one sample path on a bounded set.

引用

页码：375 / 404

页数：30

共 31 条

[1]

[Anonymous], 2002, Dynamics of Evolutionary Equations

[2]

Da Prato G., 1992, STOCHASTIC EQUATIONS

[3] Time-discretised galerkin approximations of parabolic stochastic PDES [J].