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+∞ is an entrance boundary. We give a necessary and sufficient condition for the existence of exactly one quasistationary distribution, and we also show that this distribution attracts all initial distributions.

Key words： One-dimensional diffusions; quasi-stationary distribution; Yaglom limit; quasi-limiting distribution

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