J. Jonasson, INFINITE-DIVISIBILITY OF RANDOM OBJECTS IN LOCALLY COMPACT POSITIVE CONVEX CONES, Journal of Multivariate Analysis, 65(2), 1998, pp. 129-138
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.