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

Hélène Leman (1, 2) , Juan Carlos Pardo Millan (3)

1 NUMED - Numerical Medicine
2 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées
3 CIMAT - Centro de Investigación en Matemáticas

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.

Mots clés: extinction; Continuous state branching processes in random environment; competition; coming down from infinity

Domaines: Probabilités [math.PR]

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⟩