A non-Markovian process with unbounded \(p\)-variation. (English) Zbl 1060.60074

Summary: A recent theorem by the author [Ann. Probab. 32, No. 3A, 2053–2066 (2004; Zbl 1052.60058)] provided a link between a certain function of transition probabilities of a strong Markov process and the boundedness of the \(p\)-variation of its trajectories. Here one assumption of that theorem is relaxed and an example is constructed to show that the Markov property cannot be easily dispensed with.


60J25 Continuous-time Markov processes on general state spaces
60G17 Sample path properties
60J35 Transition functions, generators and resolvents
60G40 Stopping times; optimal stopping problems; gambling theory


Zbl 1052.60058
Full Text: DOI EuDML