Markov branching processes with immigration-migration and resurrection

作者：Li JunPing^*; Liu ZaiMing

来源：Science China Mathematics, 2011, 54(5): 1043-1062.

DOI：10.1007/s11425-010-4156-7

• Markov branching process
• immigration
• migration
• resurrection
• regularity
• extinction
• recurrence
• ergodicity

We consider a modified Markov branching process incorporating with both state-independent immigration-migration and resurrection. The effect of state-independent immigration-migration is firstly investigated in detail. The explicit expressions for the extinction probabilities and mean extinction times are presented. The ergodicity and stability properties of the process incorporating with resurrection structure are then investigated. The conditions for recurrence, ergodicity and exponential ergodicity are obtained. An explicit expression for the equilibrium distribution is also presented. As a preparation, the criteria for regularity and uniqueness for such structure are firstly established.

• 出版日期2011-5
• 单位中南大学