Quasistationary distributions for one-dimensional diffusions with singular boundary points

In the present work we characterize the existence of quasistationary distributions for diffusions on (0, infinity) allowing singular behavior at 0 and infinity. If absorption at 0 is certain, we show that there exists a quasistationary distribution as soon as the spectrum of the generator is strictly positive. This complements results of Cattiaux et al. (2009) and Kolb and Steinsaltz (2012) for 0 being a regular boundary point and extends results by Cattiaux et al. (2009) on singular diffusions. (C) 2018 Elsevier B.V. All rights reserved.