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Multivariate subordination, self-decomposability and stability

Part of: Distribution theory - Probability Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Ole E. Barndorff-Nielsen ,
Jan Pedersen  and
Ken-Iti Sato
Ole E. Barndorff-Nielsen*
Affiliation:
MaPhySto and University of Aarhus
Jan Pedersen*
Affiliation:
University of Aarhus
Ken-Iti Sato*
Affiliation:
University of Aarhus
*
∗ Postal address: Department of Mathematical Sciences, University of Aarhus, Ny Munkegade, DK-8000 Aarhus C, Denmark.
∗ Postal address: Department of Mathematical Sciences, University of Aarhus, Ny Munkegade, DK-8000 Aarhus C, Denmark.
∗∗ Email address: oebn@imf.au.dk
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Abstract

Multivariate subordinators are multivariate Lévy processes that are increasing in each component. Various examples of multivariate subordinators, of interest for applications, are given. Subordination of Lévy processes with independent components by multivariate subordinators is defined. Multiparameter Lévy processes and their subordination are introduced so that the subordinated processes are multivariate Lévy processes. The relations between the characteristic triplets involved are established. It is shown that operator self-decomposability 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.

Keywords

Levy processesmultiparameter Levy processesmultivariate subordinationoperator self-decomposabilityoperator stability

MSC classification

Primary: 60G51: Processes with independent increments; L'evy processes
Secondary: 60E07: Infinitely divisible distributions; stable distributions

Information

Type
General Applied Probability
Information
Advances in Applied Probability , Volume 33 , Issue 1 , March 2001 , pp. 160 - 187
Copyright
Copyright © Applied Probability Trust 2001 

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