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Moments of additive martingales of branching Lévy processes and applications
Yan-Xia Ren, Renming Song, Rui Zhang · 2025-09-11 · via math.PR updates on arXiv.org

Let $W_t(θ)$ be the Biggins martingale of a supercritical branching Lévy process with non-local branching mechanism, and denote by $W_\infty(θ)$ its limit. In this paper, we first study moment properties of $W_t(θ)$ and $W_\infty(θ)$, and the tail behavior of $W_\infty(θ)$. We then apply these results to establish central limit theorems for $W_t(θ)-W_\infty(θ)$.

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