ON THE CONVEX HULL OF SYMMETRIC STABLE PROCESSES

Let alpha is an element of (1,2] and X be an R-d-valued symmetric alpha-stable Levy process starting at 0. We 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 of this paper 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 -> 0. For this we assume that X has independent components.