Stationary distributions of multivariate diffusion processes have recently been proposed as probabilistic models of causal systems in statistics and machine learning. Motivated by these developments, we study stationary multivariate diffusion processes with a sparsely structured drift. Our main result gives a characterization of the conditional independence relations that hold in a stationary distribution. The result draws on a graphical representation of the drift structure and pertains to conditional independence relations that hold generally as a consequence of the drift's sparsity pattern.

翻译：多元扩散过程的平稳分布最近被提出作为统计学和机器学习中因果系统的概率模型。受这些进展的启发，我们研究了具有稀疏结构漂移的平稳多元扩散过程。我们的主要结果给出了平稳分布中成立的条件独立性关系的特征刻画。该结果借鉴了漂移结构的图形表示，并涉及那些作为漂移稀疏性模式的普遍结果而成立的条件独立性关系。