An accurate, efficient, and conceptually simple method is developed to estimate distributions of maxima of solutions of stochastic equations, i.e., ordinary or partial differential equations with random entries. The method is data-based. It constructs importance sampling (IS) or biasing measures from samples of surrogates of full model solutions of stochastic equations and uses these measures and mixtures of surrogate and full model samples to estimate probabilities of extreme events. Numerical examples are presented to illustrate the implementations of the proposed method and demonstrate numerically its performance.

中文翻译：

---

基于数据的极端事件重要性抽样估计

开发了一种准确，有效且概念上简单的方法来估计随机方程（即具有随机入口的常微分方程或偏微分方程）的解的最大值的分布。该方法是基于数据的。它从随机方程的完整模型解决方案的替代样本中构造出重要性抽样（IS）或偏差度量，并使用这些度量以及替代样本与完整模型样本的混合来估计极端事件的概率。数值例子说明了该方法的实现，并从数值上证明了其性能。