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

Published online by Cambridge University Press:  25 February 2021

H. Leman
Affiliation:
Université de Lyon, Inria, CNRS, ENS de Lyon, UMPA
J. C. Pardo
Affiliation:
Centro de Investigación en Matemáticas A.C.
Corresponding
E-mail address:

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.

Type
Research Papers
Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Applied Probability Trust

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