This article studies a general divide-and-conquer algorithm for approximating continuous one-dimensional probability distributions with finite mean. The article presents a numerical study that compares pre-existing approximation schemes with a special focus on the stability of the discrete approximations when they undergo arithmetic operations. The main results are a simple upper bound of the approximation error in terms of the Wasserstein-1 distance that is valid for all continuous distributions with finite mean. In many use-cases, the studied method achieve optimal rate of convergence, and numerical experiments show that the algorithm is more stable than pre-existing approximation schemes in the context of arithmetic operations.

翻译：本文研究一种通用的分治算法，用于逼近具有有限均值的一维连续概率分布。文章通过数值研究比较了现有逼近方案，特别关注离散逼近在经历算术运算时的稳定性。主要成果是给出了适用于所有具有有限均值的连续分布的逼近误差上界，该上界以Wasserstein-1距离表示。在许多应用场景中，所研究的方法达到了最优收敛速率，数值实验表明该算法在算术运算背景下比现有逼近方案具有更好的稳定性。