Noncausality and Marginalization of Markov Processes
证明马尔可夫过程的子过程在满足非因果性条件时也是马尔可夫的，并分析了时间范围（有限或无限）对非因果性的影响，给出了相关条件与反例。
In this paper it is shown that a subprocess of a Markov process is markovian if a suitable condition of noncausality is satisfied. Furthermore, a markovian condition is shown to be a natural condition when analyzing 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 also given to illustrate the cases where these further conditions are not satisfied.