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Journal Articles Journal of Applied Probability Year : 2021

Extinction and coming down from infinity of continuous-state branching processes with competition in a Lévy environment

Abstract

We are interested in the property of coming down from infinity of continuous-state branching processes with competition in a Lévy environment. We first study the event of extinction for such a family of processes under Grey’s condition. Moreover, if we add an integrability condition on the competition mechanism then the process comes down from infinity regardless of the long-time behaviour of the environment.
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Dates and versions

hal-01694581 , version 1 (27-01-2018)
hal-01694581 , version 2 (05-11-2018)
hal-01694581 , version 3 (04-10-2019)

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Hélène Leman, Juan Carlos Pardo Millan. Extinction and coming down from infinity of continuous-state branching processes with competition in a Lévy environment. Journal of Applied Probability, 2021, 58 (1), pp.128 - 139. ⟨10.1017/jpr.2020.77⟩. ⟨hal-01694581v3⟩
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