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arXiv · 2509.09188

Moments of additive martingales of branching L\'evy processes and applications

Yan-Xia Ren·Renming Song·Rui Zhang
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Abstract

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

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Yan-Xia Ren, Renming Song, Rui Zhang. 2025-09-11. Moments of additive martingales of branching L\'evy processes and applications. https://arxiv.org/abs/2509.09188

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