Besov Regularity of Stochastic Integrals with Respect to the Fractional Brownian Motion with Parameter H > 1/2期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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

Authors:	David Nualart Youssef Ouknine

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

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 ^t₀u_sB_s belong to the Besov space _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 p2 and for some large enough, then the trajectories of the indefinite divergence integral ^t₀u_sB_s belong to the Besov space _p,^H.

Keywords:	fractional Brownian motion stochastic integrals Malliavin calculus
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