Quasi-Stationary Distributions and Resilience: What to get from a sample? - Département de mathématiques appliquées Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2019

Quasi-Stationary Distributions and Resilience: What to get from a sample?

Résumé

We study a class of multi-species birth-and-death processes going almost surely to extinction and admitting a unique quasi-stationary distribution (qsd for short). When rescaled by K and in the limit K ! +1, the realizations of such processes get close, in any fixed finite-time window, to the trajectories of a dynamical system whose vector field is defined by the birth and death rates. Assuming that this dynamical has a unique attracting fixed point, we analyzed in a previous work what happens for large but finite K, especially the different time scales showing up. In the present work, we are mainly interested in the following question: Observing a realization of the process, can we determine the so-called engineering resilience? To answer this question, we establish two relations which intermingle the resilience, which is a macroscopic quantity defined for the dynamical system, and the fluctuations of the process, which are microscopic quantities. Analogous relations are well known in nonequilibrium statistical mechanics. To exploit these relations, we need to introduce several estimators which we control for times between log K (time scale to converge to the qsd) and $\exp(K)$ (time scale of mean time to extinction).
Fichier principal
Vignette du fichier
resilience43.pdf (480.83 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-02167101 , version 1 (03-07-2019)
hal-02167101 , version 2 (17-09-2019)
hal-02167101 , version 3 (19-06-2020)

Identifiants

  • HAL Id : hal-02167101 , version 2

Citer

Jean-René Chazottes, Pierre Collet, Servet Martínez, Sylvie Méléard. Quasi-Stationary Distributions and Resilience: What to get from a sample?. 2019. ⟨hal-02167101v2⟩
171 Consultations
97 Téléchargements

Partager

Gmail Facebook X LinkedIn More