论文标题
Seneta-Heyde规范，用于分支随机步行，$α$稳定的脊柱
Seneta-Heyde norming for branching random walks with $α$-stable spine
论文作者
论文摘要
我们考虑在吸引$α$稳定的莱维过程的领域中带有脊柱的随机步行。在此过程中，通常在极限下退化的经典衍生品曲棍球。我们首先确定替代衍生物玛格莱尔的数量，并表明在某些LLOGL型条件下，它会收敛到非脱位极限，我们认为这是最佳的。我们继续在相同的假设下为关键的添加剂玛特宁格提供了塞内塔·赫德的规范。证明是基于我们以前的论文中介绍的方法，该论文考虑了有限差异案例[Boutaud and Maillard（2019），EJP，第1卷。 24，纸编号。 99]。
We consider branching random walks with a spine in the domain of attraction of an $α$-stable Lévy process. For this process, the classical derivative martingale in general degenerates in the limit. We first determine the quantity replacing the derivative martingale and show that it converges to a non-degenerate limit under a certain LlogL-type condition which we assume to be optimal. We go on to give the Seneta-Heyde norming for the critical additive martingale under the same assumptions. The proofs are based on the methods introduced in our previous paper which considered the finite variance case [Boutaud and Maillard (2019), EJP, vol. 24, paper no. 99].
