Quasi-stationary distributions of one-dimensional generalized diffusions without natural boundaries

This paper provides sufficient criteria for the existence and uniqueness as well as characterisations for the domain of attraction of quasi-stationary distributions (QSDs) of one-dimensional generalized diffusions without natural boundaries. In particular, it is shown that if the associated transition density is intrinsically ultracontractive, the underlying diffusion is uniformly conditionally ergodic and hence possesses a unique QSD which attracts exponentially and uniformly all probability measures.