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	UNIVERSITY OF WROCŁAW

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	WROCŁAW UNIVERSITY OF SCIENCE AND TECHNOLOGY

Contents of PMS, Vol. 41, Fasc. 2, pages 303 - 320
`DOI: 10.37190/0208-4147.41.2.6`
`Published online 7.9.2021`

On the Besov regularity of the bifractional Brownian~motion Brahim Boufoussi Yassine Nachit Abstract: Our aim is to improve Hölder continuity results for the bifractional Brownian motion (bBm) $(B^{α, β} (t))_{t \in [0, 1]}$ with $0 < α < 1$ and $0 < β \leq 1$ . We prove that almost all paths of the bBm belong to (resp. do not belong to) the Besov spaces $Bes (α β, p)$ (resp. $bes (α β, p)$ ) for any $\frac{1}{α β} < p < \infty$ , where $bes (α β, p)$ is a separable subspace of $Bes (α β, p)$ . We also show similar regularity results in the Besov-Orlicz space $Bes (α β, M_{2})$ with $M_{2} (x) = e^{x^{2}} - 1$ . We conclude by proving the Ito-Nisio theorem for the bBm with $α β > 1 / 2$ in the Hölder spaces $C^{γ}$ with $γ < α β$ . 2010 AMS Mathematics Subject Classification: Primary 60G15; Secondary 60G18, 60G17. Keywords and phrases: bifractional Brownian motion, self-similar, Besov spaces, Besov--Orlicz spaces, Itô--Nisio.
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