Besov Regularity of Stochastic Integrals with Respect to the Fractional Brownian Motion with Parameter H > 1/2 |
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Authors: | David Nualart Youssef Ouknine |
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Affiliation: | (1) Facultat de Matemàtiques, Universitat de Barcelona, Gran Via Corts Catalanes 585, 08007 Barcelona, Spain;(2) Faculté des Sciences Semlalia, Département de Mathématiques, Université Cadi Ayyad, BP 2390, Marrakech, Morocco |
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Abstract: | Let {Bt,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 t0us Bs belong to the Besov space p,q for all , provided the integrand u belongs to the space . Moreover, if u is bounded and belongs to for some even integer p 2 and for some large enough, then the trajectories of the indefinite divergence integral t0us Bs belong to the Besov space p, H. |
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Keywords: | fractional Brownian motion stochastic integrals Malliavin calculus |
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