2019
DOI: 10.1080/15326349.2019.1575754
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Branching processes in varying environment with generation-dependent immigration

Abstract: A branching process in varying environment with generation-dependent immigration is a modification of the standard branching process in which immigration is allowed and the reproduction and immigration laws may vary over the generations. This flexibility makes the process more appropriate to model real populations due to the fact that the stability in the reproductive capacity and in the immigration laws are not usually fulfilled. In this setting, we study the extinction problem, providing a necessary and suff… Show more

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Cited by 9 publications
(3 citation statements)
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“…to random walks on trees, as in [18]) and has recently received a renewal of interest, see e.g. [2,4,13,20]. Former research on branching processes in a varying environment was temporarily affected by the appearence of certain exotic properties, and one could get the impression that it is difficult to grasp some kind of generic behaviour of these processes.…”
Section: Introduction and Main Resultsmentioning
confidence: 99%
“…to random walks on trees, as in [18]) and has recently received a renewal of interest, see e.g. [2,4,13,20]. Former research on branching processes in a varying environment was temporarily affected by the appearence of certain exotic properties, and one could get the impression that it is difficult to grasp some kind of generic behaviour of these processes.…”
Section: Introduction and Main Resultsmentioning
confidence: 99%
“…Moreover, he showed the convergence in distribution for both sequences {µ n ρ 0,n /2 : n ≥ 0} and {E[Z n | Z n > 0] : n ≥ 0}. An extension in the presence of immigration and the same setting as Kersting's has been established in [5]. All these authors established the exponential convergence using an analytical approach.…”
Section: Introduction and Main Resultsmentioning
confidence: 97%
“…Kersting [6] provided yet another proof in a similar framework to ours, that we will explain below. An extension in the presence of immigration and the same setting as Kersting's has been established in [4]. All these authors established the exponential convergence using an analytical approach.…”
Section: Introductionmentioning
confidence: 99%