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The local long-time behaviour for continuous-time branching processes

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  • Li, Liuyan
  • Li, Junping

Abstract

Let {Z(t);t≥0} be a continuous-time branching process. There is a normalizing function γt such that Z(t)γt converges almost surely to a random variable. In this paper, we obtain a local limit theorem for {Z(t);t≥0}, which refers to the asymptotic behaviour of P(Z(t)=kt) with limt→∞ktγt=x and x>0. This expands the existing results of the discrete-time branching processes.

Suggested Citation

  • Li, Liuyan & Li, Junping, 2025. "The local long-time behaviour for continuous-time branching processes," Statistics & Probability Letters, Elsevier, vol. 223(C).
    • Handle: RePEc:eee:stapro:v:223:y:2025:i:c:s0167715225000574
    DOI: 10.1016/j.spl.2025.110412
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    References listed on IDEAS

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    1. Cohn, H. & Hering, H., 1983. "Inhomogeneous Markov branching processes: Supercritical case," Stochastic Processes and their Applications, Elsevier, vol. 14(1), pages 79-91, January.
    2. Liuyan Li & Junping Li, 2023. "The Local Limit Theorem for Supercritical Branching Processes with Immigration," Journal of Theoretical Probability, Springer, vol. 36(1), pages 331-347, March.
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