Besov regularity for the indefinite Skorohod integral with respect to the fractional Brownian motion: the singular case

 

Hassan Lakhel1)   Youssef Ouknine1)   Ciprian A. Tudor2)
1) Université Cadi Ayyad, Faculté des Sciences Semlalia, B.P. 2390, Marrakech, Maroc.
2) Département de Mathématiques, Université de La Rochelle, Avenue Michel Crépau, 17042 La Rochelle Cedex 1, France.

Abstract:

Using the techniques of the Malliavin calculus and the properties of Gaussian processes, we prove that the paths of the indefinite Skorohod integral with respect to the fractional Brownian motion with Hurst parameter less than $ \frac{1}{2} $ belongs to the Besov space $ {\cal{B}}^{H}_{p, \infty }$, for any $ p>\frac{1}{H}$.

Key words: Fractional Brownian motion, Stochastic integrals, Malliavin calculus.
Mathematics Subject Classification: 60H05, 60H07.

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