论文标题
正交随机变量的有效弱欧拉山类型近似方案非常高维SDE
An efficient weak Euler-Maruyama type approximation scheme of very high dimensional SDEs by orthogonal random variables
论文作者
论文摘要
对于高维SDE，我们将介绍由正交系统在$ l^{2} [0,1] $中给出的Euler-Maruyama近似值，这可能是SPDES的有限维近似值。通常，尺寸越高，在数值模拟中，每个时间步骤都需要生成统一的随机数所需的越高。相比之下，本文提出的方案可以通过在每个时间步骤产生很少的均匀随机数来解决这个问题。这些方案节省了非常高维SDE的模拟时间。特别是，我们得出的结论是，基于沃尔什系统的Euler-Maruyama近似在高维度上是有效的。
We will introduce Euler-Maruyama approximations given by an orthogonal system in $L^{2}[0,1]$ for high dimensional SDEs, which could be finite dimensional approximations of SPDEs. In general, the higher the dimension is, the more one needs to generate uniform random numbers at every time step in numerical simulation. The schemes proposed in this paper, in contrast, can deal with this problem by generating very few uniform random numbers at every time step. The schemes save time in the simulation of very high dimensional SDEs. In particular, we conclude that an Euler-Maruyama approximation based on the Walsh system is efficient in high dimensions.
