期刊名称：Brazilian Journal of Probability and Statistics
印刷版ISSN：0103-0752
出版年度：2019
卷号：33
期号：2
页码：356-373
DOI：10.1214/18-BJPS391
语种：English
出版社：Brazilian Statistical Association
摘要：Consider a supercritical branching random walk on the real line. The consistent maximal displacement is the smallest of the distances between the trajectories followed by individuals at the $n$th generation and the boundary of the process. Fang and Zeitouni, and Faraud, Hu and Shi proved that under some integrability conditions, the consistent maximal displacement grows almost surely at rate $\lambda^{*}n^{1/3}$ for some explicit constant $\lambda^{*}$. We obtain here a necessary and sufficient condition for this asymptotic behaviour to hold.
