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Some properties of 2-type Markov branching processes with immigration and instantaneous resurrection

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  • Meng, Weiwei
  • Xi, Chengxun

Abstract

We consider a modified 2-type Markov branching processes incorporating with both immigration and instantaneous resurrection. We prove that if the sum of the immigration rates is finite then no such structure can exist. The existence criterion is presented for the case that the sum of the resurrection rates is infinite. We construct some equivalent criteria that are far easier to verify. The recurrence and ergodicity criterion of the researching process are analysed in detail. The explicit expression for the equilibrium distribution is also presented.

Suggested Citation

  • Meng, Weiwei & Xi, Chengxun, 2022. "Some properties of 2-type Markov branching processes with immigration and instantaneous resurrection," Statistics & Probability Letters, Elsevier, vol. 189(C).
    • Handle: RePEc:eee:stapro:v:189:y:2022:i:c:s0167715222001250
    DOI: 10.1016/j.spl.2022.109571
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    References listed on IDEAS

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    1. Li, Junping & Meng, Weiwei, 2017. "Regularity criterion for 2-type Markov branching processes with immigration," Statistics & Probability Letters, Elsevier, vol. 121(C), pages 109-118.
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