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

Martynas Manstavicius (University of Connecticut, USA)


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.

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Pages: 17-28

Publication Date: February 25, 2005

DOI: 10.1214/ECP.v10-1128


  1. J. R. Kinney. Continuity properties of sample functions of Markov processes. Trans. Amer. Math. Soc. 74 (1953), 280--302. Math. Review MR0053428
  2. E. B. Dynkin. Criteria of continuity and of absence of discontinuities of the second kind for trajectories of a Markov random process. Izv. Akad. Nauk SSSR Ser. Mat. 16 (1952), 563--572, (in Russian). Math. Review MR0052055
  3. M. Manstavicius. The p-variation of strong Markov processes. Ann. Probab. 32(2004), no. 3A, 2053-2066. Math. Review MR2073185
  4. R. M. Dudley and R. Norvaisa. An Introduction to p-Variation and Young Integrals. Maphysto Lecture notes 1 (1998, revised 1999) (pdf file) Math. Review number not available.

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