On the convex hull of symmetric stable processes (Q2845067)

The object of this paper is an \(\mathbb R^d\)-valued symmetric \(\alpha\)-stable Lévy process starting at the origin. The authors consider the closure \(S_t\) of the path described by \(X\) on the interval \([0, t]\) and its convex hull \(Z_t\). The first result provides a formula for certain mean mixed volumes of \(Z_t\), and in particular for the expected first intrinsic volume of \(Z_t\). The second result deals with the asymptotics of the expected volume of the stable sausage \(Z_t+B\) (where \(B\) is an arbitrary convex body with interior points) as \(t\to0\). For this, the authors assume that \(X\) has independent components.