A unifying approach to non-minimal quasi-stationary distributions for one-dimensional diffusions

Abstract

Convergence to non-minimal quasi-stationary distributions for one-dimensional diffusions is studied. We give a method of reducing the convergence to the tail behavior of the lifetime via a property which we call the first hitting uniqueness. We apply the results to Kummer diffusions with negative drifts and give a class of initial distributions converging to each non-minimal quasi-stationary distribution.