Asymptotic behaviors of subcritical branching killed Lévy processes

2025/03/05 by Yan-Xia Ren, Renming Song, Ren, Yan-Xia +3
Business, Management and Accounting · Economics, Econometrics and Finance · Mathematics · #Advanced Queuing Theory Analysis #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2503.03580

openalex publication_date 2025/03/05 · openalex created_date 2025/10/22 · openalex updated_date 2026/07/29

Abstract

In this paper, we investigate the asymptotic behaviors of the survival probability and maximal displacement of a subcritical branching killed Lévy process X in ℝ. Let ζ denote the extinction time, M_t be the maximal position of all the particles alive at time t, and M:=sup_{t≥ 0}M_t be the all-time maximum. Under the assumption that the offspring distribution satisfies the Llog L condition and some conditions on the spatial motion, we find the decay rate of the survival probability ℙ_x(ζ>t) and the tail behavior of M_t as t→∞. As a consequence, we establish a Yaglom-type theorem. We also find the asymptotic behavior of ℙ_x(M>y) as y→∞.

Related

• Tails of extinction time and maximal displacement for critical branching killed Lévy process
• Maximal displacement of spectrally negative branching Lévy processes
• Asymptotic behaviors of subcritical branching killed Brownian motion with drift
• Speed of extinction for continuous state branching processes in subcritical Lévy environments: the strongly and intermediate regimes
• Tail probability of maximal displacement in critical branching Lévy process with stable branching