NONCAUSALITY AND MARGINALIZATION OF MARKOV-PROCESSES

In this paper it is shown that a subprocess of a Markov process is mar kovian if a suitable condition of noncausality is satisfied. Furthermo re, a markovian condition is shown to be a natural condition when anal yzing the role of the horizon (finite or infinite) in the property of noncausality. We also give further conditions implying that a process is both jointly and marginally markovian only if there is both finite and infinite noncausality and that a process verifies both finite and infinite noncausality only if it is markovian. Counterexamples are als o given to illustrate the cases where these further conditions are not satisfied.