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aug 2006 Quasi-stationary distributions for Lévy processes
Andreas E. Kyprianou, Zbigniew Palmowski
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Bernoulli 12(4): 571-581 (aug 2006). DOI: 10.3150/bj/1155735927


In recent years there has been some focus in work by Bertoin, Chaumont and Doney on the behaviour of one-dimensional Lévy processes and random walks conditioned to stay positive. The resulting conditioned process is transient. In earlier literature, however, one encounters for special classes of random walks and Lévy processes a similar, but nonetheless different, type of asymptotic conditioning to stay positive which results in a limiting quasi-stationary distribution. We extend this theme into the general setting of a Lévy process fulfilling certain types of conditions which are analogues of known classes in the random walk literature. Our results generalize those of E.K. Kyprianou for special types of one-sided compound Poisson processes with drift and of Martínez and San Martín for Brownian motion with drift, and complement the results due to Iglehart, Doney, and Bertoin and Doney for random walks.


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Andreas E. Kyprianou. Zbigniew Palmowski. "Quasi-stationary distributions for Lévy processes." Bernoulli 12 (4) 571 - 581, aug 2006.


Published: aug 2006
First available in Project Euclid: 16 August 2006

zbMATH: 1130.60054
MathSciNet: MR2248228
Digital Object Identifier: 10.3150/bj/1155735927

Keywords: Conditioning , fluctuation theory , Lévy processes , quasi-stationary distribution

Rights: Copyright © 2006 Bernoulli Society for Mathematical Statistics and Probability


Vol.12 • No. 4 • aug 2006
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