AN ELEMENTARY RENEWAL THEOREM FOR RANDOM COMPACT CONVEX-SETS

A set-valued analog of the elementary renewal theorem for Minkowski su ms of random closed sets is considered. The corresponding renewal func tion is defined as [GRAPHICS] where S-n=A(1)+...+A(n) are Minkowski (e lement-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 contai ning the origin as an interior point, [GRAPHICS] where h(K)(u) is the support function of K and S-A(+) is the set of all unit vectors u with Eh(A)(u)>0. Other set-valued generalizations of the renewal function are also suggested.