Galton-Watson processes in dynamical environments
Dynamical Systems
2024-10-28 v1 Probability
Abstract
We define a model of Galton Watson processes in dynamical environments where the environment evolves according to a dynamical system (X, T). Three behaviours are possible: uniformly subcritical, critical, and uniformly supercritical. We study the extinction probability q in the uniformly supercritical case. In particular, we investigate the regularity of this application as a function of the environment x. In the critical case, we study the set of bad environments N (where the probability of extinction is one), which is T -invariant. We give its Hausdorff dimension in some cases.
Cite
@article{arxiv.2410.19327,
title = {Galton-Watson processes in dynamical environments},
author = {Thomas Morand},
journal= {arXiv preprint arXiv:2410.19327},
year = {2024}
}