论文标题
具有多重Lipschitz噪声的热方程的有限体积方案的收敛
Convergence of a finite-volume scheme for a heat equation with a multiplicative Lipschitz noise
论文作者
论文摘要
在这里，我们在这里研究了有限体积方案的近似值，该方程是由Lipschitz迫使Lipschitz连续乘法噪声强迫的近似方案。更确切地说，我们考虑了一个半径的离散化，而空间中的两点通量近似方案（TPFA）。我们基于Prokhorov的定理来调整该方法以获得分布结果的收敛性，然后Skorokhod的表示定理产生了该方案向Martingale解决方案的收敛性，并且使用Gyöngy-Krylov参数来证明与我们使用Parabolic问题的独特变性解决方案的方案的概率相融合。
We study here the approximation by a finite-volume scheme of a heat equation forced by a Lipschitz continuous multiplicative noise in the sense of Itô. More precisely, we consider a discretization which is semi-implicit in time and a two-point flux approximation scheme (TPFA) in space. We adapt the method based on the theorem of Prokhorov to obtain a convergence in distribution result, then Skorokhod's representation theorem yields the convergence of the scheme towards a martingale solution and the Gyöngy-Krylov argument is used to prove convergence in probability of the scheme towards the unique variational solution of our parabolic problem.
