Geodesic
Life-Periods of a Branching Process with Immigration
Teoriâ veroâtnostej i ee primeneniâ, Tome 17 (1972) no. 1, pp. 179-188

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The life-period of a branching process with immigration is a time interval for which the number of particles remains positive. We obtain asymptotic formulas for the tails of the distribution functions of life-periods and find necessary and sufficient conditions for the state 0 of the corresponding Markov chain to be recurrent. 
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     author = {A. M. Zubkov},
     title = {Life-Periods of a {Branching} {Process} with {Immigration}},
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A. M. Zubkov. Life-Periods of a Branching Process with Immigration. Teoriâ veroâtnostej i ee primeneniâ, Tome 17 (1972) no. 1, pp. 179-188. http://geodesic.mathdoc.fr/item/TVP_1972_17_1_a17/