Convex hulls of stable random walks

Abstract

We consider convex hulls of random walks whose steps belong to the domain of attraction of a stable law in Rd. We prove convergence of the convex hull in the space of all convex and compact subsets of Rd, equipped with the Hausdorff distance, towards the convex hull spanned by a path of the limit stable Lévy process. As an application, we establish convergence of (expected) intrinsic volumes under some mild moment/structure assumptions posed on the random walk.