We study a class of graphs that represent local independence structures in stochastic processes allowing for correlated error processes. Several graphs may encode the same local independencies and we characterize such equivalence classes of graphs. In the worst case, the number of conditions in our characterizations grows superpolynomially as a function of the size of the node set in the graph. We show that deciding Markov equivalence is coNP-complete which suggests that our characterizations cannot be improved upon substantially. We prove a global Markov property in the case of a multivariate Ornstein-Uhlenbeck process which is driven by correlated Brownian motions.

翻译：我们研究一组图表,这些图表代表了本地独立结构的随机过程,允许相关的错误过程。几个图表可能编码相同的本地不依赖性,我们将这种等同的图表类别定性为。最坏的情况是,我们定性中的条件数量随着图中设定的节点大小的函数而超极化增长。我们表明,确定Markov等值是共同NP的完成,这表明我们的定性无法大大改进。在由相关布朗运动驱动的多变Ornstein-Uhlenbeck进程的情况下,我们证明了全球的Markov属性。