论文标题
对退化抛物线 - 纤维pde的有限差异方案的收敛速度和征费噪声
On rate of convergence of finite difference scheme for degenerate parabolic-hyperbolic PDE with Levy noise
论文作者
论文摘要
在本文中，我们考虑了一个半离散的有限差差方案，该方案是由Lévy噪声在一个空间维度中驱动的退化抛物线式碳酸盐PDE。 Using bounded variation estimations and a variant of classical Kružkov's doubling of variable approach, we prove that expected value of the $L^1$-difference between the unique entropy solution and approximate solution converges at a rate of $(Δx)^\frac{1}{7}$, where $Δx$ is the spatial mesh size.
In this article, we consider a semi discrete finite difference scheme for a degenerate parabolic-hyperbolic PDE driven by Lévy noise in one space dimension. Using bounded variation estimations and a variant of classical Kružkov's doubling of variable approach, we prove that expected value of the $L^1$-difference between the unique entropy solution and approximate solution converges at a rate of $(Δx)^\frac{1}{7}$, where $Δx$ is the spatial mesh size.
