Explosion of continuous-state branching processes with competition in L\'evy environment

TL;DR

This paper establishes criteria for explosion and nonexplosion in continuous-state branching processes with competition within a Lévy environment, focusing on power competition functions and stable Lévy measures.

Contribution

It provides necessary and sufficient conditions for explosion behavior in these processes, advancing understanding of their long-term dynamics.

Findings

Criteria for explosion and nonexplosion identified

Conditions specific to power competition functions

Results applicable to stable Lévy measures

Abstract

Using the Lyapunov criteria arguments, we find sufficient conditions on explosion/nonexplosion for continuous-state branching processes with competition in L\'evy random environment. In particular, we identify the necessary and sufficient conditions on explosion/nonexplosion when the competition function is a power function and the L\'evy measure of the associated branching mechanism is stable.