On convex hull of d-dimensional fractional Brownian motion

Abstract

It is well known that for standard Brownian motion $ \{B(t), \;t \geq 0\}$ with values in $\mathbb{R}^d$ its convex hull $ V(t)=\conv \{\{\,B(s),\;s \leq t \}$ with probability 1 contains 0 as an interior point for each $t > 0$ (see \cite{E}). The aim of this note is to state the analoguos property for $d$-dimensional fractional Brownian motion.