论文标题
非线性SPDE的数值近似
Numerical Approximation of Nonlinear SPDE's
论文作者
论文摘要
对随机抛物线偏微分方程的数值分析进行了$$ du + a（u）= f \，dt + g \，dw，$$的数值分析，其中$ a $是部分操作员，而布朗尼运动。该手稿将过去十年中的许多理论统一为一个有内聚的框架，该框架将确定性偏微分方程近似的技术与随机普通微分方程的近似方法进行了近似。手稿旨在访问这些学科中的任何一个的观众，并提供了例子来说明该理论的适用性。
The numerical analysis of stochastic parabolic partial differential equations of the form $$ du + A(u) = f \,dt + g \, dW, $$ is surveyed, where $A$ is a partial operator and $W$ a Brownian motion. This manuscript unifies much of the theory developed over the last decade into a cohesive framework which integrates techniques for the approximation of deterministic partial differential equations with methods for the approximation of stochastic ordinary differential equations. The manuscript is intended to be accessible to audiences versed in either of these disciplines, and examples are presented to illustrate the applicability of the theory.
