Seneta-Heyde norming for branching random walks with $\alpha$-stable spine - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2021

Seneta-Heyde norming for branching random walks with $\alpha$-stable spine

Résumé

We consider branching random walks with a spine in the domain of attraction of an $\alpha$-stable L\'evy 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].

Dates et versions

hal-03292334 , version 1 (20-07-2021)

Identifiants

Citer

Pierre Boutaud, Pascal Maillard. Seneta-Heyde norming for branching random walks with $\alpha$-stable spine. 2021. ⟨hal-03292334⟩
13 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More