Biggins' martingale convergence for branching Lévy processes

DOI10.1214/18-ECP185zbMath1402.60051arXiv1712.04769MaRDI QIDQ1994112

Bastien Mallein, Jean Bertoin

Publication date: 1 November 2018

Published in: Electronic Communications in Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1712.04769

zbMATH Keywords

uniform integrabilityadditive martingalespinal decompositionbranching Lévy process

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Martingales with continuous parameter (60G44) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

Related Items (9)

Maximal displacement of spectrally negative branching Lévy processes ⋮ On the law of terminal value of additive martingales in a remarkable branching stable process ⋮ Solutions of kinetic-type equations with perturbed collisions ⋮ Biggins' martingale convergence for branching Lévy processes ⋮ Self-similar solutions of kinetic-type equations: the boundary case ⋮ Branching-stable point measures and processes ⋮ A result on power moments of L\'evy-type perpetuities and its application to the $L_p$-convergence of Biggins' martingales in branching L\'evy processes ⋮ Probability tilting of compensated fragmentations ⋮ A necessary and sufficient condition for the convergence of the derivative martingale in a branching Lévy process

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