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 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 Lévy-Khinchin representation for a generalized Laplace transform. The result generalizes the classical Lévy-Khinchin representation for non-negative random variables and the corresponding result for random compact convex sets inRn. 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.
Volume (Year): 65 (1998)
Issue (Month): 2 (May)
|Contact details of provider:|| Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description|
|Order Information:|| Postal: http://www.elsevier.com/wps/find/supportfaq.cws_home/regional|
When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:65:y:1998:i:2:p:129-138. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Shamier, Wendy)
If references are entirely missing, you can add them using this form.