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A Remark on the 1/H-Variation of the Fractional Brownian Motion

Part of the Lecture Notes in Mathematics book series (SEMPROBAB,volume 2006)

Abstract

We give an elementary proof of the following property of H-fractional Brownian motion: almost all sample paths have infinite 1/H-variation on every interval.

  • Fractional Brownian motion
  • p-Variation
  • Ergodic theorem

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Correspondence to Maurizio Pratelli .

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Pratelli, M. (2011). A Remark on the 1/H-Variation of the Fractional Brownian Motion. In: Donati-Martin, C., Lejay, A., Rouault, A. (eds) Séminaire de Probabilités XLIII. Lecture Notes in Mathematics(), vol 2006. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15217-7_8

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