论文标题
随机热方程的密度近似的收敛性
Convergence of Density Approximations for Stochastic Heat Equation
论文作者
论文摘要
本文研究了均匀收敛拓扑和总变化距离中随机热方程的密度近似的收敛性。在非线性情况下，均匀收敛拓扑的密度的收敛顺序恰好是$ 1/2 $，在线性案例中差不多$ 1 $。该结果意味着近似值的分布总是在总变化距离内收敛到原点方程的分布。据我们所知，这是密度近似与随机部分微分方程的收敛性的第一个结果。
This paper investigates the convergence of density approximations for stochastic heat equation in both uniform convergence topology and total variation distance. The convergence order of the densities in uniform convergence topology is shown to be exactly $1/2$ in the nonlinear case and nearly $1$ in the linear case. This result implies that the distributions of the approximations always converge to the distribution of the origin equation in total variation distance. As far as we know, this is the first result on the convergence of density approximations to the stochastic partial differential equation.
