We study the exponential growth of branching processes with ancestral dependence. We suppose here that the lifetimes of the cells are dependent random variables, that the numbers of new cells are random and dependent. Lifetimes and new cells’s numbers are also assumed to be dependent. Applying the spectral study of Laplace-type operators recently made in Hervé et al. [ESAIM: PS 23 (2019) 607–637], we illustrate our results in the Markov context, for which the exponential growth property is linked to the Laplace transform of the lifetimes of the cells.
Accepté le :
DOI : 10.1051/ps/2019001
Mots-clés : Markov processes, quasi-compactness, operator, perturbation, ergodicity, Laplace transform, branching process, age-dependent process, Malthusian parameter
@article{PS_2019__23__584_0,
author = {Herv\'e, Lo{\"\i}c and Louhichi, Sana and P\`ene, Fran\c{c}oise},
title = {Exponential growth of branching processes in a general context of lifetimes and birthtimes dependence},
journal = {ESAIM: Probability and Statistics},
pages = {584--606},
publisher = {EDP-Sciences},
volume = {23},
year = {2019},
doi = {10.1051/ps/2019001},
mrnumber = {4011568},
zbl = {1506.60067},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ps/2019001/}
}
TY - JOUR AU - Hervé, Loïc AU - Louhichi, Sana AU - Pène, Françoise TI - Exponential growth of branching processes in a general context of lifetimes and birthtimes dependence JO - ESAIM: Probability and Statistics PY - 2019 SP - 584 EP - 606 VL - 23 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ps/2019001/ DO - 10.1051/ps/2019001 LA - en ID - PS_2019__23__584_0 ER -
%0 Journal Article %A Hervé, Loïc %A Louhichi, Sana %A Pène, Françoise %T Exponential growth of branching processes in a general context of lifetimes and birthtimes dependence %J ESAIM: Probability and Statistics %D 2019 %P 584-606 %V 23 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ps/2019001/ %R 10.1051/ps/2019001 %G en %F PS_2019__23__584_0
Hervé, Loïc; Louhichi, Sana; Pène, Françoise. Exponential growth of branching processes in a general context of lifetimes and birthtimes dependence. ESAIM: Probability and Statistics, Tome 23 (2019), pp. 584-606. doi : 10.1051/ps/2019001. http://archive.numdam.org/articles/10.1051/ps/2019001/
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