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It is well known that for a standard Brownian motion (BM) $ \{B(t), \;t \geq0\}$ with values in $\mathbb{R}^d$, its convex hull $ V(t)=\conv \{\{\,B(s),\;s\leq t \}$ with probability $1$ for each $t > 0$ contains $0$ as an interiorpoint (see Evans (1985)). We also know that the winding number of a typicalpath of a $2$-dimensional BM is equal to $+\infty.$  The aim of this article is to show that these properties aren't specifically"Brownian", but hold for a much larger class of $d$-dimensional self similarprocesses. This class contains in particular $d$-dimensional fractionalBrownian motions and (concerning convex hulls) strictly stable Levy processes.

On convex hull and winding number of self similar processes