On Deterministic Markov Processes: Expandability and Related Topics

A. Schnurr

2013, v.19, №4, 693-720

ABSTRACT

We analyze the class of universal Markov processes on $R^d$ which do not depend on random. For this, as well as for several subclasses, we prove criteria whether a function $f:[0,\infty[ \to R^d$ can be a path of a process in the respective class. This is useful in particular in the construction of (counter-) examples. 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'.

Keywords: Markov semimartingale,deterministic process,Ito process,Feller process,symbol,expandability

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