On the quasi-stationary distribution for some randomly perturbed transformations of an interval
type: Item
instance of: scholarly article
title: On the quasi-stationary distribution for some randomly perturbed transformations of an interval
zbMATH Open document ID: 0942.60070
author: Fima Klebaner
author: Justin Lazar
author: Ofer Zeitouni
published in: The Annals of Applied Probability
publication date: 2000-08-16T00:00:00Z
review text: The authors consider a continuous piecewise \(C^2\) map \(f\) of the unit interval \(I\) into itself with \(f(x)<1 \forall x\in I\) whose limit set consists of a finite number of stable and unstable fixed points. Next, they study quasi-stationary distributions of small random perturbations of \(f\) and show that under some conditions these distributions concentrate around stable fixed points. An application to density dependent branching processes is given.
Mathematics Subject Classification ID: 60J80
Mathematics Subject Classification ID: 60F10
zbMATH DE Number: 1319855
zbMATH Keywords: large deviations
zbMATH Keywords: logistic map
zbMATH Keywords: branching systems
reviewed by: Yuri Kifer
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aoap/1027961045
OpenAlex ID: W2095585229
cites work: Q5624436
cites work: Q4365545
cites work: On the quasi-stationary distribution of a stochastic Ricker model
cites work: Principal eigenvalues, topological pressure, and stochastic stability of equilibrium states
cites work: Population-dependent branching processes with a threshold
cites work: Autoregressive approximation in branching processes with a threshold
cites work: The exit problem for a class of density-dependent branching systems
cites work: Simple mathematical models with very complicated dynamics
DOI: 10.1214/AOAP/1027961045
description: scientific article; zbMATH DE number 1319855