Implicit scheme for stochastic parabolic partial differential equations driven by space-time white noise

被引：59

作者：

Gyongy, I ^{[1
]}

Nualart, D ^{[1
]}

机构：

[1] UNIV BARCELONA,FAC MATEMAT,E-08007 BARCELONA,SPAIN

来源：

POTENTIAL ANALYSIS | 1997年 / 7卷 / 04期

关键词：

stochastic partial differential equations; space-time white noise; implicit approximation;

D O I：

10.1023/A:1017998901460

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We extend Rothe's method of solving linear parabolic PDEs to the case of nonlinear SPDEs driven by space-time white noise. When the nonlinear terms are Lipschitz functions we prove almost sure convergence of the approximations uniformly in time and space. When the nonlinear drift term is only measurable we obtain the convergence in probability, by using Malliavin calculus.

引用

页码：725 / 757

页数：33

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