SIAM/ASA Journal on Uncertainty Quantification, Volume 9, Issue 1, Page 135-162, January 2021.
A probabilistic approach to estimating sample qualities of stochastic differential equations is introduced in this paper. The aim is to provide a quantitative upper bound of the distance between the invariant probability measure of a stochastic differential equation and that of its numerical approximation. In order to extend estimates of finite time truncation error to infinite time, it is crucial to know the rate of contraction of the transition kernel of the SDE. We find that suitable numerical coupling methods can effectively estimate such rate of contraction, which gives the distance between two invariant probability measures. Our algorithms are tested with several low and high dimensional numerical examples.

中文翻译：

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使用耦合方法估计随机微分方程的样本质量

SIAM / ASA不确定性量化杂志，第9卷，第1期，第135-162页，2021年1月
。本文介绍了一种估计随机微分方程样本质量的概率方法。目的是提供随机微分方程的不变概率测度与其数值逼近之间的距离的定量上限。为了将有限时间截断误差的估计扩展到无限时间，了解SDE过渡内核的收缩率至关重要。我们发现合适的数值耦合方法可以有效地估计这种收缩率，从而给出两个不变概率测度之间的距离。我们的算法已通过几个低维和高维数值示例进行了测试。