In this paper, we combine deterministic splitting methods with a polynomial chaos expansion method for solving stochastic parabolic evolution problems. The stochastic differential equation is reduced to a system of deterministic equations that we solve efficiently by splitting methods. The method can be applied to a wide class of problems where the related stochastic processes are given uniquely in terms of stochastic polynomials. A comprehensive convergence analysis is provided and numerical experiments validate our approach.

中文翻译：

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随机演化方程的分裂/多项式混沌展开方法

在本文中，我们将确定性分裂方法与多项式混沌展开法相结合来解决随机抛物线演化问题。随机微分方程简化为确定性方程组，我们可以通过拆分方法有效地对其进行求解。该方法可以应用于各种各样的问题，其中根据随机多项式唯一地给出了相关的随机过程。提供了全面的收敛性分析，数值实验验证了我们的方法。