论文标题
在一段时间内生成随机热方程的完全离散的样品时
On generating fully discrete samples of the stochastic heat equation on an interval
论文作者
论文摘要
概括了戴维和盖恩斯（Davie and Gaines）（2001）的概念，我们提出了一种在间隔中模拟完全离散的溶液样本到随机热方程的方法。我们提供了近似值的有效性的条件，该条件尤其是在时间和空间观测趋于无穷大时。因此，近似的质量以总变化距离进行测量。在一项仿真研究中，我们计算了通过我们的方法和过程的幼稚截断来产生的样本路径的时间和空间二次变化。在此，我们方法提供的结果更准确，计算成本较低。
Generalizing an idea of Davie and Gaines (2001), we present a method for the simulation of fully discrete samples of the solution to the stochastic heat equation on an interval. We provide a condition for the validity of the approximation, which holds particularly when the number of temporal and spatial observations tends to infinity. Hereby, the quality of the approximation is measured in total variation distance. In a simulation study we calculate temporal and spatial quadratic variations from sample paths generated both via our method and via naive truncation of the Fourier series representation of the process. Hereby, the results provided by our method are more accurate at a considerably lower computational cost.
