On the Besov regularity of the bifractional Brownian motion

Brahim Boufoussi; Yassine Nachit

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arXiv · 2007.05780

On the Besov regularity of the bifractional Brownian motion

Brahim Boufoussi·Yassine Nachit

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Abstract

Our aim in this paper is to improve H\"{o}lder continuity results for the bifractional Brownian motion (bBm) $(B^{\alpha,\beta}(t))_{t\in[0,1] }$ with $0<\alpha<1$ and $0<\beta\leq 1$. We prove that almost all paths of the bBm belong (resp. do not belong) to the Besov spaces $\mathbf{Bes}(\alpha \beta,p)$ (resp. $\mathbf{bes}(\alpha \beta,p)$) for any $\frac{1}{\alpha \beta} \frac{1}{2}$ in the H\"{o}lder spaces $\mathcal{C}^{\gamma}$, with $\gamma<\alpha \beta$.

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Brahim Boufoussi, Yassine Nachit. 2020-07-11. On the Besov regularity of the bifractional Brownian motion. https://arxiv.org/abs/2007.05780

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