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Finite Variation of Fractional Lévy Processes

Author

Listed:
  • Christian Bender

    (Universität des Saarlandes)

  • Alexander Lindner

    (Technische Universität Braunschweig)

  • Markus Schicks

    (Technische Universität Braunschweig)

Abstract

Various characterizations for fractional Lévy processes to be of finite variation are obtained, one of which is in terms of the characteristic triplet of the driving Lévy process, while others are in terms of differentiability properties of the sample paths. A zero-one law and a formula for the expected total variation are also given.

Suggested Citation

  • Christian Bender & Alexander Lindner & Markus Schicks, 2012. "Finite Variation of Fractional Lévy Processes," Journal of Theoretical Probability, Springer, vol. 25(2), pages 594-612, June.
    • Handle: RePEc:spr:jotpro:v:25:y:2012:i:2:d:10.1007_s10959-010-0339-y
    DOI: 10.1007/s10959-010-0339-y
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    References listed on IDEAS

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    1. Basse, Andreas & Pedersen, Jan, 2009. "Lévy driven moving averages and semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 119(9), pages 2970-2991, September.
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    Cited by:

    1. Bender, Christian & Knobloch, Robert & Oberacker, Philip, 2015. "A generalised Itō formula for Lévy-driven Volterra processes," Stochastic Processes and their Applications, Elsevier, vol. 125(8), pages 2989-3022.

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