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Packing measure of the sample paths of fractional Brownian motion

Authors:	Yimin Xiao

Institution:	Department of Mathematics, The Ohio State University, Columbus, Ohio 43210

Abstract:	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 such that with probability 1, $\begin{displaymath}\hbox { $\phi $-$p(X(0,t]))$} = Kt \ \hbox {for any } t > 0 ,\end{displaymath}$ where $% \phi (s) = s^{\frac 1 {% \alpha }}/ (\log \log \frac 1 s)^{\frac 1 {2 % \alpha }}$ and $\phi$ - is the $\phi$ -packing measure of .

Keywords:	Packing measure fractional Brownian motion image sojourn time

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