论文标题
在平均和扩散近似方案中的一类随机微分方程的渐近保存方案上
On Asymptotic Preserving schemes for a class of Stochastic Differential Equations in averaging and diffusion approximation regimes
论文作者
论文摘要
我们介绍并研究了一类缓慢快速的随机微分方程的渐近保留方案的概念，该概念与分布收敛有关。在某些示例中，原始方案无法捕获由平均和扩散近似程序产生的正确限制方程。我们提出了渐近保存方案的示例：当时间尺度的分离消失时，就会获得限制方案，该方案与限制随机微分方程的分布一致。数值实验说明了在几个示例中提出的渐近保存方案的重要性。另外，在平均方面，获得了错误估计，并证明提出的方案是统一准确的。
We introduce and study a notion of Asymptotic Preserving schemes, related to convergence in distribution, for a class of slow-fast Stochastic Differential Equations. In some examples, crude schemes fail to capture the correct limiting equation resulting from averaging and diffusion approximation procedures. We propose examples of Asymptotic Preserving schemes: when the time-scale separation vanishes, one obtains a limiting scheme, which is shown to be consistent in distribution with the limiting Stochastic Differential Equation. Numerical experiments illustrate the importance of the proposed Asymptotic Preserving schemes for several examples. In addition, in the averaging regime, error estimates are obtained and the proposed scheme is proved to be uniformly accurate.
