Bernoulli

  • Bernoulli
  • Volume 12, Number 4 (2006), 571-581.

Quasi-stationary distributions for Lévy processes

Andreas E. Kyprianou and Zbigniew Palmowski

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Abstract

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.

Article information

Source
Bernoulli, Volume 12, Number 4 (2006), 571-581.

Dates
First available in Project Euclid: 16 August 2006

Permanent link to this document
https://projecteuclid.org/euclid.bj/1155735927

Digital Object Identifier
doi:10.3150/bj/1155735927

Mathematical Reviews number (MathSciNet)
MR2248228

Zentralblatt MATH identifier
1130.60054

Keywords
conditioning fluctuation theory Lévy processes quasi-stationary distribution

Citation

Kyprianou, Andreas E.; Palmowski, Zbigniew. Quasi-stationary distributions for Lévy processes. Bernoulli 12 (2006), no. 4, 571--581. doi:10.3150/bj/1155735927. https://projecteuclid.org/euclid.bj/1155735927


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