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 $\frac{ 1}{ \alpha \beta}<p<\infty$, where $\mathbf{ bes}(\alpha \beta,p)$ is a separable subspace of $\mathbf{ Bes}(\alpha \beta,p)$. We also show the It\^{ o}-Nisio theorem for the bBm with $\alpha \beta>\frac{ 1}{ 2}$ in the H\"{ o}lder spaces $\mathcal{ C}^{ \gamma}$, with $\gamma<\alpha \beta$.
Categories: math.PR