A Non-Markovian Process with Unbounded $p$-Variation

Abstract

A recent theorem by M. Manstavicius (2004) 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.