Domain of attraction of quasi-stationary distribution for   one-dimensional diffusions
  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. 
Hanjun Zhang and Guoman He
math.PR