Positive hulls of random walks and bridges

Abstract

We study random convex cones defned as positive hulls of $d$-dimensional random walks and bridges. We compute expectations of various geometric functionals of these cones such as the number of $k$-dimensional faces and the sums of conic quermassintegrals of their $k$-dimensional faces. These expectations are expressed in terms of Stirling numbers of both kinds and their $B$-analogues.