Nauchno-issledovatelskiy Institut Tekhnologii Avtomobilnoy Promyshlennosti

A set-valued analog of the elementary renewal theorem for Minkowski sums of random closed sets is considered. The corresponding renewal function is defined as where are Minkowski (element-wise) sums of i.i.d. random compact convex sets. In this paper we determine the limit of H(tK)/t as t tends to infinity. For K containing the origin as an interior point, where hK (u) is the support function of K and is the set of all unit vectors u with EhA (u) > 0. Other set-valued generalizations of the renewal function are also suggested.