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

Weiwei Meng and Chengxun Xi

Statistics & Probability Letters, 2022, vol. 189, issue C

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.

Keywords: 2-type Markov branching process; Immigration; Instantaneous resurrection; Existence; Ergodicity (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spl.2022.109571

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