数学物理学报 ›› 2009, Vol. 29 ›› Issue (2): 303-315.

• 论文 • 上一篇    下一篇

带移民Jirina过程的弱极限定理

李育强   

  1. (华东师范大学金融与统计学院 上海 200241)
  • 收稿日期:2007-03-21 修回日期:2008-12-14 出版日期:2009-04-25 发布日期:2009-04-25
  • 基金资助:

    国家自然科学基金(10771070)资助.

Weak Limit Theorems for Ji\v{r}ina Processes with Immigration

Li Yuqiang   

  1. (School of Finance and Statistics, East China Normal University, Shanghai 200241)
  • Received:2007-03-21 Revised:2008-12-14 Online:2009-04-25 Published:2009-04-25
  • Supported by:

    国家自然科学基金(10771070)资助.

摘要:

该文在矩条件下讨论了一列带移民Ji\rina过程的弱极限定理.  按照极限过程的不同对矩条件作了简单分类.  文章证明了在不同的矩条件下, 一列带移民Ji\rina过程适当规范后可以在Skorokhod空间分别弱收敛到连续分支过程,  带移民的连续分支过程, 不连续的带移民分支过程以及确定性过程. 对最后这种情形,还给出了一个波动极限定理.

关键词: 带移民的Ji\rina过程, 带移民的连续分支过程, Ornstein-Uhlenbeck过程, 弱收敛

Abstract:

The author studies the limit theorems of Ji\v{r}ina processes with immigration under moment conditions. The moment conditions are classified according to the limiting processes. It is proved that under different moment conditions, a sequence of scaled Ji\v{r}ina processes with immigration converges weakly in the Skorokhod space to the continuous branching process, the continuous branching process with immigration, the branching
process with immigration with jumps and the deterministic process, respectively. For the last case, a fluctuation limit theorem is also proved.

Key words: Ji\rina process with immigration, Continuous branching process with immigration, Ornstein-Uhlenbeck process, Weak convergence

中图分类号: 

  • 60J80