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.

Reproduction of initial distributions from the first hitting time distribution for birth-and-death processes

“…In [13], we have studied quasi-stationary distributions of one-dimensional diffusions. Let X be a d dm d ds -diffusion on S := [0, b) (0 < b ≤ ∞) stopped at 0.…”