Packing measure of the sample paths of fractional Brownian motion

Let $X(t) (t \in % \mathbf {R})$ be a fractional Brownian motion of index $% \alpha$ in $% \mathbf {R}^d.$ If $1 < % \alpha d$, then there exists a positive finite constant $K$ such that with probability 1,

where $% \phi (s) = s^{\frac 1 {% \alpha }}/ (\log \log \frac 1 s)^{\frac 1 {2 % \alpha }}$ and $\phi$-$p (X([0,t]))$ is the $\phi$-packing measure of $X([0,t])$.