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Besov Regularity of Stochastic Integrals with Respect to the Fractional Brownian Motion with Parameter H > 1/2

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Listed:
  • David Nualart

    (Universitat de Barcelona)

  • Youssef Ouknine

    (Université Cadi Ayyad)

Abstract

Let {B t ,t∈[0,1]} be a fractional Brownian motion with Hurst parameter H > 1/2. Using the techniques of the Malliavin calculus we show that the trajectories of the indefinite divergence integral ∫ t 0 u s δB s belong to the Besov space ℬ p,q α for all $$q \geqslant 1,\frac{1}{p}

Suggested Citation

  • David Nualart & Youssef Ouknine, 2003. "Besov Regularity of Stochastic Integrals with Respect to the Fractional Brownian Motion with Parameter H > 1/2," Journal of Theoretical Probability, Springer, vol. 16(2), pages 451-470, April.
    • Handle: RePEc:spr:jotpro:v:16:y:2003:i:2:d:10.1023_a:1023530929480
    DOI: 10.1023/A:1023530929480
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    References listed on IDEAS

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    1. Mémin, Jean & Mishura, Yulia & Valkeila, Esko, 2001. "Inequalities for the moments of Wiener integrals with respect to a fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 51(2), pages 197-206, January.
    2. Alòs, Elisa & Mazet, Olivier & Nualart, David, 2000. "Stochastic calculus with respect to fractional Brownian motion with Hurst parameter lesser than," Stochastic Processes and their Applications, Elsevier, vol. 86(1), pages 121-139, March.
    3. W. Dai & C. C. Heyde, 1996. "Itô's formula with respect to fractional Brownian motion and its application," International Journal of Stochastic Analysis, Hindawi, vol. 9, pages 1-10, January.
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