2011/11/08 by Alexander Schnurr, Schnurr, Alexander
Economics, Econometrics and Finance · Mathematics · #47G30 (Secondary) #60J25 (Primary) 60J35 #60J75 #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and financial applications #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.1111.1912
openalex publication_date 2011/11/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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'.