On the Limit Distributions of Continuous-State Branching Processes with Immigration

Details On the Limit Distributions of Continuous-State Branching Processes with Immigration On the Limit Distributions of Continuous-State Branching Processes with Immigration

2011-03-29

arxiv.org/abs/1103.5605v3

Mathematics

Probability

minor update; to appear in SPA

Scientific paper

We consider the class of continuous-state branching processes with immigration (CBI-processes), introduced by Kawazu and Watanabe (1971) and their limit distributions as time tends to infinity. We determine the Levy-Khintchine triplet of the limit distribution and give an explicit description in terms of the characteristic triplets of the Levy subordinator and the spectrally positive Levy 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 characterise its absolute continuity and asymptotic behavior at the boundary of the support, generalizing several known results on self-decomposable distributions.

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