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

Liuyan Li and Junping Li

Statistics & Probability Letters, 2025, vol. 223, issue C

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.

Keywords: Local long-time behaviour; Continuous-time branching processes; Branching Q-matrix (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spl.2025.110412

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