Slow recurrent regimes for a class of one-dimensional stochastic growth models

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:128

Article

Adam, Etienne¹ 

[1] Univ Paris Saclay, CNRS, Ecole Polytech, CMAP, Route Saclay, F-91128 Palaiseau, France

关键词: Markov chains;    Hitting-times;    Recurrence classification;    Lyapunov function;    Stochastic difference equation;   

DOI  :  10.1016/j.spa.2017.10.005

来源: Elsevier

【 摘 要 】

We classify the possible behaviors of a class of one-dimensional stochastic recurrent growth models. In our main result, we obtain nearly optimal bounds for the tail of hitting times of some compact sets. If the process is an aperiodic irreducible Markov chain, we determine whether it is null recurrent or positive recurrent and in the latter case, we obtain a subgeometric convergence of its transition kernel to its invariant measure. We apply our results in particular to state-dependent Galton-Watson processes and we give precise estimates of the tail of the extinction time. (C) 2017 Published by Elsevier B.V.

【 授权许可】

Free