Convergence to non-minimal quasi-stationary distributions for one-dimensional diffusions and its application to Kummer diffusions (Probability Symposium)

Abstract

We summarize the following results of the author's recent work [17] without proof. For one-dimensional diffusions killed at the boundaries, the domain of attraction of non-minimal quasi-stationary distributions is studied. We give a general 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 result to Kummer diffusions with negative drifts and clarify the domain of attraction of each non-minimal quasi-stationary distribution for the processes.