We study the speed of extinction of continuous state branching processes in a Lévy environment, where the associated Lévy process oscillates. Assuming that the Lévy process satisfies Spitzer’s condition, we extend recent results where the associated branching mechanism is stable. The study relies on the path analysis of the branching process together with its Lévy environment, when the latter is conditioned to have a non-negative running infimum. For that purpose, we combine the approach developed in Afanasyev et al. [2], for the discrete setting and i.i.d. environments, with fluctuation theory of Lévy processes and a result on exponential functionals of Lévy processes due to Patie and Savov [28].
Keywords: Continuous state branching processes, Lévy processes conditioned to stay positive, random environment, Spitzer’s condition, extinction, long time behaviour
@article{PS_2021__25_1_346_0,
author = {Bansaye, Vincent and Pardo, Juan Carlos and Smadi, Charline},
title = {Extinction rate of continuous state branching processes in critical {L\'evy} environments},
journal = {ESAIM: Probability and Statistics},
pages = {346--375},
year = {2021},
publisher = {EDP-Sciences},
volume = {25},
doi = {10.1051/ps/2021014},
mrnumber = {4291369},
zbl = {1482.60112},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ps/2021014/}
}
TY - JOUR AU - Bansaye, Vincent AU - Pardo, Juan Carlos AU - Smadi, Charline TI - Extinction rate of continuous state branching processes in critical Lévy environments JO - ESAIM: Probability and Statistics PY - 2021 SP - 346 EP - 375 VL - 25 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/ps/2021014/ DO - 10.1051/ps/2021014 LA - en ID - PS_2021__25_1_346_0 ER -
%0 Journal Article %A Bansaye, Vincent %A Pardo, Juan Carlos %A Smadi, Charline %T Extinction rate of continuous state branching processes in critical Lévy environments %J ESAIM: Probability and Statistics %D 2021 %P 346-375 %V 25 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/ps/2021014/ %R 10.1051/ps/2021014 %G en %F PS_2021__25_1_346_0
Bansaye, Vincent; Pardo, Juan Carlos; Smadi, Charline. Extinction rate of continuous state branching processes in critical Lévy environments. ESAIM: Probability and Statistics, Tome 25 (2021), pp. 346-375. doi: 10.1051/ps/2021014
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