Domain of attraction of quasi-stationary distribution for one-dimensional diffusions

Abstract

We study quasi-stationarity for one-dimensional diffusions killed at 0, when 0 is a regular boundary and $+\infty$ is an entrance boundary. We give a necessary and sufficient condition for the existence of exactly one quasi-stationary distribution, and we also show that this distribution attracts all initial distributions.Comment: This paper is published in Frontiers of Mathematics in China (2016