Graphical modeling of stochastic processes driven by correlated noise

We study a class of graphs that represent local independence structures in stochastic processes allowing for corre-lated noise processes. Several graphs may encode the same local independencies and we characterize such equiv-alence classes of graphs. In the worst case, the number of conditions in our characterizations grows superpolyno-mially as a function of the size of the node set in the graph. We show that deciding Markov equivalence of graphs from this class 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.

Automated summary

We examine a class of graphs that represent local independence structures in stochastic processes with correlated noise. We classify graphs that encode the same local independencies and show that determining Markov equivalence for this class of graphs is a complex task. Additionally, we prove the global Markov property for a specific multivariate process.