We show that any stochastic differential equation with prescribed time-dependent marginal distributions admits a decomposition into three components: a unique scalar field governing marginal evolution, a symmetric positive-semidefinite diffusion matrix field and a skew-symmetric matrix field.

翻译：我们证明，任何具有给定时间依赖边际分布的随机微分方程均可分解为三个组成部分：控制边际演化的唯一标量场、对称半正定扩散矩阵场和斜对称矩阵场。