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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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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 α p,q for all \(q \geqslant 1,\frac{1}{p} < \alpha < H\), provided the integrand u belongs to the space \(\mathbb{L}^{p,1} \). Moreover, if u is bounded and belongs to \(\mathbb{L}^{\delta ,2} \) for some even integer p≥2 and for some δ large enough, then the trajectories of the indefinite divergence integral ∫t 0 u s δB s belong to the Besov space ℬ Hp,∞ .

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Authors and Affiliations

  1. Facultat de Matemàtiques, Universitat de Barcelona, Gran Via Corts Catalanes 585, 08007, Barcelona, Spain

    David Nualart

  2. Faculté des Sciences Semlalia, Département de Mathématiques, Université Cadi Ayyad, BP 2390, Marrakech, Morocco

    Youssef Ouknine

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  1. David Nualart
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  2. Youssef Ouknine
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Nualart, D., Ouknine, Y. Besov Regularity of Stochastic Integrals with Respect to the Fractional Brownian Motion with Parameter H > 1/2. Journal of Theoretical Probability 16, 451–470 (2003). https://doi.org/10.1023/A:1023530929480

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