Explosion of continuous-state branching processes with competition in Lévy environment
arXiv:2205.07415
Abstract
Using the Lyapunov criteria arguments, we find sufficient conditions on explosion/nonexplosion for continuous-state branching processes with competition in Lévy random environment. In particular, we identify the necessary and sufficient conditions on explosion/nonexplosion when the competition function is a power function and the Lévy measure of the associated branching mechanism is stable.