On convex hull of d-dimensional fractional Brownian motion

Abstract

It is well known that for standard Brownian motion $\{B(t),t\ge 0\}$ 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.

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