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On the limit distributions of continuous-state branching processes with immigration
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Keller-Ressel, Martin and Mijatović, Aleksandar (2012) On the limit distributions of continuous-state branching processes with immigration. Stochastic Processes and their Applications, Vol.122 (No.6). pp. 2329-2345. doi:10.1016/j.spa.2012.03.012 ISSN 0304-4149.
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Official URL: http://dx.doi.org/10.1016/j.spa.2012.03.012
Abstract
We consider the class of continuous-state branching processes with immigration (CBI-processes), introduced by Kawazu and Watanabe (1971) [10] and their limit distributions as time tends to infinity. We determine the Lévy-Khintchine triplet of the limit distribution and give an explicit description in terms of the characteristic triplet of the Lévy subordinator and the scale function of the spectrally positive Lévy process, which describe the immigration resp. branching mechanism of the CBI-process. This representation allows us to describe the support of the limit distribution and characterize its absolute continuity and asymptotic behavior at the boundary of the support, generalizing several known results on self-decomposable distributions. © 2012 Elsevier B.V. All rights reserved.
Item Type: | Journal Article | ||||
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Subjects: | H Social Sciences > HA Statistics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||
Journal or Publication Title: | Stochastic Processes and their Applications | ||||
Publisher: | Elsevier Science BV | ||||
ISSN: | 0304-4149 | ||||
Official Date: | June 2012 | ||||
Dates: |
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Volume: | Vol.122 | ||||
Number: | No.6 | ||||
Page Range: | pp. 2329-2345 | ||||
DOI: | 10.1016/j.spa.2012.03.012 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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