On convex hull of d-dimensional fractional Brownian motion

Details On convex hull of d-dimensional fractional Brownian motion On convex hull of d-dimensional fractional Brownian motion

2011-05-30

arxiv.org/abs/1105.6018v1

Mathematics

Probability

Scientific paper

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.

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