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Centre for Mathematical Physics and Stochastics
Department of Mathematical Sciences, University of Aarhus

Funded by The Danish National Research Foundation

MPS-RR 2000-28
July 2000

Multivariate Subordination, Selfdecomposability and Stability


Ole E. Barndorff-Nielsen

Jan Pedersen, Ken-iti Sato


Multivariate subordinators are multivariate Levy processes that are increasing in each component. Various examples of multivariate subordinators, of interest for applications, are given. Subordination of Levy processes with independent components by multivariate subordinators is defined. Multiparameter Levy processes and their subordination are introduced so that the subordinated processes are multivariate Levy processes. The relations between the characteristic triplets involved are established. It is shown that operator selfdecomposability and the operator version of the class $L_m$ property are inherited from the multivariate subordinator to the subordinated process under the condition of operator stability of the subordinand.

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This paper has now been published in Adv. Appl. Prob. 33, (2001), 160-187.