Bertoin, Jean, Exponential decay and ergodicity of completely asymmetric Lévy processes in a finite interval, Annals of applied probability , 7(1), 1997, pp. 156-169
Consider a completely asymmetric Lévy process which has absolutely continuous transition probabilities. We determine the exponential decay parameter . and the quasistationary distribution for the transition probabilities of the Lévy process killed as it exits from a finite interval, prove that the killed process is .-positive and specify the .-invariant function and measure.