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 https://static.cambridge.org/content/id/urn%3Acambridge.org%3Aid%3Aarticle%3AS0001867800047741/resource/name/S0001867800047741_eqnU1.gif?pub-status=live where https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20180209072836984-0241:S0001867800047741:S0001867800047741_inline1.gif?pub-status=live 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, https://static.cambridge.org/content/id/urn%3Acambridge.org%3Aid%3Aarticle%3AS0001867800047741/resource/name/S0001867800047741_eqnU2.gif?pub-status=live 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.