1 results
An elementary renewal theorem for random compact convex sets
- Part of
-
- Journal:
- Advances in Applied Probability / Volume 27 / Issue 4 / December 1995
- Published online by Cambridge University Press:
- 01 July 2016, pp. 931-942
- Print publication:
- December 1995
-
- Article
- Export citation
-
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.
are Minkowski (element-wise) sums of i.i.d. random compact convex sets. In this paper we determine the limit of 
is the set of all unit vectors 