In this paper we present a scheme for the numerical solution of one-dimensional stochastic differential equations (SDEs) whose drift belongs to a fractional Sobolev space of negative regularity (a subspace of Schwartz distributions). We obtain a rate of convergence in a suitable $L^1$-norm and we implement the scheme numerically. To the best of our knowledge this is the first paper to study (and implement) numerical solutions of SDEs whose drift lives in a space of distributions. As a byproduct we also obtain an estimate of the convergence rate for a numerical scheme applied to SDEs with drift in $L^p$-spaces with $p\in(1,\infty)$.

翻译：在本文中,我们提出了一个单维随机差分方程式的数字解决方案,该方程式的漂移属于负常态微小索博勒夫空间(施瓦茨分布的子空间),我们以适当的1美元为单位获得趋同率,我们用数字执行这个方案。据我们所知,这是研究(和实施)在分布空间中漂移生命的SDE的数值解决方案的第一份文件。作为副产品,我们还获得了对以1美元(1美元)为单位漂移在1美元/美元空间的SDE的数值组合率的估计。