Asymmetric separation for local independence graphs
  Directed possibly cyclic graphs have been proposed by Didelez (2000) and
Nodelmann et al. (2002) in order to represent the dynamic dependencies among
stochastic processes. These dependencies are based on a generalization of
Granger-causality to continuous time, first developed by Schweder (1970) for
Markov processes, who called them local dependencies. They deserve special
attention as they are asymmetric unlike stochastic (in)dependence. In this
paper we focus on their graphical representation and develop a suitable, i.e.
asymmetric notion of separation, called delta-separation. The properties of
this graph separation as well as of local independence are investigated in
detail within a framework of asymmetric (semi)graphoids allowing a deeper
insight into what information can be read off these graphs.
