On the quasi-stationary distribution for some randomly perturbed transformations of an interval
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.
scientific article; zbMATH DE number 1319855