区间上随机heat equation的全离散样本生成
On generating fully discrete samples of the stochastic heat equation on an interval
摘要：
推广Davie和Gaines（2001）的思想，我们提出了一种在区间上模拟随机热方程解的全离散样本的方法。我们提供了一个条件的有效性的近似，特别是当时间和空间观测的数量趋于无穷大。由此，近似的质量以全变差距离来测量。在模拟研究中，我们计算时间和空间的二次变化，通过我们的方法，并通过天真的截断的傅里叶级数表示的过程中产生的样本路径。因此，我们的方法提供的结果是更准确的，在一个相当低的计算成本。
英文摘要：
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.
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