Acta mathematica scientia,Series A ›› 2009, Vol. 29 ›› Issue (2): 303-315.

• Articles • Previous Articles     Next Articles

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.

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

CLC Number: 

  • 60J80
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