Infinite Divisibility of Random Objects in Locally Compact Positive Convex Cones
✍ Scribed by Johan Jonasson
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 233 KB
- Volume
- 65
- Category
- Article
- ISSN
- 0047-259X
No coin nor oath required. For personal study only.
✦ Synopsis
Random objects taking on values in a locally compact second countable convex cone are studied. The convex cone is assumed to have the property that the class of continuous additive positively homogeneous functionals is separating, an assumption which turns out to imply that the cone is positive. Infinite divisibility is characterized in terms of an analog to the Le vy Khinchin representation for a generalized Laplace transform. The result generalizes the classical Le vy Khinchin representation for non-negative random variables and the corresponding result for random compact convex sets in R n . It also gives a characterization of infinite divisibility for random upper semicontinuous functions, in particular for random distribution functions with compact support and, finally, a similar characterization for random processes on a compact Polish space.