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The asymptotic behaviors for branching α-stable process

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  • Luan, Nana
  • Wang, Li

Abstract

We consider a branching symmetric α-stable process in which random split takes place at rate β>0. We obtain results concerning the long-term behavior of the number of particles surpassing eλt at time t for λ>0. Additionally, we derive the almost sure asymptotic speed of the rightmost particle as a consequence.

Suggested Citation

  • Luan, Nana & Wang, Li, 2025. "The asymptotic behaviors for branching α-stable process," Statistics & Probability Letters, Elsevier, vol. 220(C).
    • Handle: RePEc:eee:stapro:v:220:y:2025:i:c:s0167715225000082
    DOI: 10.1016/j.spl.2025.110362
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    References listed on IDEAS

    as
    1. Thomas Madaule, 2017. "Convergence in Law for the Branching Random Walk Seen from Its Tip," Journal of Theoretical Probability, Springer, vol. 30(1), pages 27-63, March.
    2. Chen, Xinxin, 2013. "Waiting times for particles in a branching Brownian motion to reach the rightmost position," Stochastic Processes and their Applications, Elsevier, vol. 123(8), pages 3153-3182.
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