An elementary renewal theorem for random compact convex sets

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 the authors determine the limit of as t tends to infinity. For K containing the origin as an interior point,, where hK(u) is the support function of K>a0.5<IT>and is the set of all unit vectors u with . Other set-valued generalizations of the renewal function are also suggested.