On the limit distributions of continuous-state branching processes with immigration

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• 作者：Martin Keller-Ressel^a ; ^{mkeller@math.tu-berlin.de} ; Aleksandar Mijatovi膰^b ; ^{a.mijatovic@warwick.ac.uk}
• 关键词：60G10 ; 60G51
• 刊名：Stochastic Processes and their Applications
• 出版年：2012
• 期刊代码：57_03044149
• 类别：mt
• 出版时间：June, 2012
• 卷：122
• 期：6
• 页码：2329-2345
• 文件大小：240 K

摘要

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 L茅vy-Khintchine triplet of the limit distribution and give an explicit description in terms of the characteristic triplet of the L茅vy subordinator and the scale function of the spectrally positive L茅vy process, which describe the immigration resp.聽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.