关于确定性马尔可夫过程：可扩展性及相关问题
On Deterministic Markov Processes: Expandability and Related Topics
摘要：
本文讨论了d维Euklidean空间上不依赖于随机的泛马氏过程类。对于这些，以及几个子类，我们证明标准是否函数f，定义在正半线，可以是一个过程中的相应类的路径。这在构造（反例）时特别有用。此外，我们的特点，这类过程，这是均匀的空间和时间。利用一维确定性马尔可夫过程的跳来刻画半鞅性。我们强调时间齐次和时间不齐次的情况下，我们表明，一个确定性的马尔可夫过程一般比亨特过程加“跳跃结构”的差异。
英文摘要：
We treat the class of universal Markov processes on the d-dimensional Euklidean space which do not depend on random. For these, as well as for several subclasses, we prove criteria whether a function f, defined on the positive half-line, can be a path of a process in the respective class. This is useful in particular in the construction of (counter-)examples. Furthermore we characterize the processes of this kind, which are homogeneous in space and time. The semimartingale property is characterized in terms of the jumps of a one-dimensional deterministic Markov process. We emphasize the differences between the time homogeneous and the time inhomogeneous case and we show that a deterministic Markov process is in general more complicated than a Hunt process plus 'jump structure'.
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