Explosion of continuous-state branching processes with competition in Lévy environment

2022/05/16 by Rugang Ma, Ma, Rugang, Xiaowen Zhou +1 · 2 citations
Business, Management and Accounting · Decision Sciences · Mathematics · #Advanced Queuing Theory Analysis #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2205.07415

openalex publication_date 2022/05/16 · openalex created_date 2022/05/22 · openalex updated_date 2026/07/28

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.

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• Boundary behavior of continuous-state interacting multi-type branching processes with immigration
• Extinction, explosion and contraction for time-inhomogeneous SDEs with jumps

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