@article{c6d7313e85e948eeae1d38c3f554f8a3,
title = "Weak convergence of the extremes of branching L{\'e}vy processes with regularly varying tails",
abstract = "We study the weak convergence of the extremes of supercritical branching L{\'e}vy processes whose spatial motions are L{\'e}vy processes with regularly varying tails. The result is drastically different from the case of branching Brownian motions. We prove that, when properly renormalized, converges weakly. As a consequence, we obtain a limit theorem for the order statistics of.",
keywords = "Branching L{\'e}vy process, extremal process, regularly varying, rightmost position",
author = "Ren, {Yan Xia} and Renming Song and Rui Zhang",
note = "The research of Y.-X. Ren is supported by the National Key R&D Program of China (No. 2020YFA0712900) and NSFC (Grant Nos. 12071011 and 11731009). The research of R. Song is supported by a grant from the Simons Foundation (#960480, Renming Song). Part of the research for this paper was done while R. Song was visiting Jiangsu Normal University, where he was partially supported by a grant from the National Natural Science Foundation of China (11931004, Yingchao Xie). The research of R. Zhang is supported by NSFC (Grant Nos. 11601354, 12271374, and 12371143), Beijing Municipal Natural Science Foundation (Grant No. 1202004), and the Academy for Multidisciplinary Studies, Capital Normal University.",
year = "2024",
month = jun,
day = "6",
doi = "10.1017/jpr.2023.103",
language = "English (US)",
volume = "61",
pages = "622--643",
journal = "Journal of Applied Probability",
issn = "0021-9002",
publisher = "Cambridge University Press",
number = "2",
}