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

Published 29 Sep 2014 in math.PR | (1409.8103v4)

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.

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