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

Hélène Leman | Zendy; Juan Carlos Pardo | Zendy

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

Author(s) -

Hélène Leman,

Juan Carlos Pardo

Publication year - 2021

Publication title -

journal of applied probability

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.668

H-Index - 59

eISSN - 1475-6072

pISSN - 0021-9002

DOI - 10.1017/jpr.2020.77

Subject(s) - infinity , branching (polymer chemistry) , extinction (optical mineralogy) , competition (biology) , property (philosophy) , state (computer science) , branching process , statistical physics , physics , mathematics , mathematical analysis , biology , ecology , philosophy , chemistry , epistemology , algorithm , optics , organic chemistry

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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