Association criteria for m-infinitely-divisible and u-infinitely-divisible random sets

We study random convex compact sets infinitely divisible with respect to the Minkowski addition and establish a sufficient condition for their association as well as a necessary and sufficient condition for the so-called infinite association. Further, we show also that every union infinitely-divisible random closed set and every convex compact set infinitely divisible for convex hulls of unions are associated.