Abstract
Consider a completely asymmetric Lévy process which has absolutely continuous transition probabilities. We determine the exponential decay parameter $\rho$ 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 $\rho$-positive and specify the $\rho$-invariant function and measure.
Citation
Jean Bertoin. "Exponential decay and ergodicity of completely asymmetric Lévy processes in a finite interval." Ann. Appl. Probab. 7 (1) 156 - 169, February 1997. https://doi.org/10.1214/aoap/1034625257
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