INFINITE-DIVISIBILITY OF RANDOM OBJECTS IN LOCALLY COMPACT POSITIVE CONVEX CONES

Random objects taking on values in a locally compact second countable convex cone are studied. The convex cone is assumed to have the proper ty that the class of continuous additive positively homogeneous functi onals is separating, an assumption which turns out to imply that the c one is positive. Infinite divisibility is characterized in terms of an analog to the Levy-Khinchin representation for a generalized Laplace transform. The result generalizes the classical Levy-Khinchin represen tation for non-negative random variables and the corresponding result for random compact convex sets in R-n. It also gives a characterizatio n of infinite divisibility for random upper semicontinuous functions, in particular for random distribution functions with compact support a nd, finally, a similar characterization for random processes on a comp act Polish space. (C) 1998 Academic Press.