The sector constants of continuous state branching processes with immigration

详细信息	查看全文 | 推荐本文 |

• 作者：Kenji Handa ; ^{handa@ms.saga-u.ac.jp}
• 关键词：Continuous state branching process ; Non-symmetric Dirichlet form ; Sector condition ; Generalized gamma convolution ; Stieltjes transform
• 刊名：Journal of Functional Analysis
• 出版年：2012
• 期刊代码：75_00221236
• 类别：mt
• 出版时间：15 May, 2012
• 卷：262
• 期：10
• 页码：4488-4524
• 文件大小：274 K

摘要

Continuous state branching processes with immigration are studied. We are particularly concerned with the associated (non-symmetric) Dirichlet form. After observing that gamma distributions are only reversible distributions for this class of models, we prove that every generalized gamma convolution is a stationary distribution of the process with suitably chosen branching mechanism and with continuous immigration. For such non-reversible processes, the strong sector condition is discussed in terms of a characteristic called the Thorin measure. In addition, some connections with notion from non-commutative probability theory will be pointed out through calculations involving the Stieltjes transform.