The method of occupation kernels has been used to learn ordinary differential equations from data in a non-parametric way. We propose a two-step method for learning the drift and diffusion of a stochastic differential equation given snapshots of the process. In the first step, we learn the drift by applying the occupation kernel algorithm to the expected value of the process. In the second step, we learn the diffusion given the drift using a semi-definite program. Specifically, we learn the diffusion squared as a non-negative function in a RKHS associated with the square of a kernel. We present examples and simulations.

翻译：占据核方法已被用于以非参数方式从数据中学习常微分方程。本文提出一种两步法，用于根据过程快照学习随机微分方程的漂移项与扩散项。第一步，通过对过程期望值应用占据核算法来学习漂移项。第二步，在给定漂移项的情况下，通过半定规划学习扩散项。具体而言，我们将扩散项的平方作为与核平方相关联的再生核希尔伯特空间中的非负函数进行学习。文中给出了具体算例与仿真结果。