Local independence graphs for composable Markov processes

The concept of local independence is used to define local
independence graphs representing the dynamic dependence structure
of several continuous time processes which jointly form a so-called
composable Markov process. Specific properties of this new class of
graphs are discussed such as the role of separating sets. Further
insight is gained by considering possible extensions to the
discrete time situation. It is shown that the latter case can be
reduced to classical graphical interaction models.