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Branching processes with immigration in a random environment—The Grincevičius–Grey setup

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  • Kevei, Péter

Abstract

We determine the tail asymptotics of the stationary distribution of a branching process with immigration in a random environment, when the immigration distribution dominates the offspring distribution. The assumptions are the same as in the Grincevičius–Grey theorem for the stochastic recurrence equation.

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  • Kevei, Péter, 2024. "Branching processes with immigration in a random environment—The Grincevičius–Grey setup," Statistics & Probability Letters, Elsevier, vol. 214(C).
    • Handle: RePEc:eee:stapro:v:214:y:2024:i:c:s0167715224001688
    DOI: 10.1016/j.spl.2024.110199
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    References listed on IDEAS

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    1. Robert, Christian Y. & Segers, Johan, 2008. "Tails of random sums of a heavy-tailed number of light-tailed terms," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 85-92, August.
    2. Barczy, Mátyás & Bősze, Zsuzsanna & Pap, Gyula, 2018. "Regularly varying non-stationary Galton–Watson processes with immigration," Statistics & Probability Letters, Elsevier, vol. 140(C), pages 106-114.
    3. Kevei, Péter & Wiandt, Péter, 2021. "Moments of the stationary distribution of subcritical multitype Galton–Watson processes with immigration," Statistics & Probability Letters, Elsevier, vol. 173(C).
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