Quasi-stationary distributions for Lévy processes

A. E. Kyprianou, Z. Palmowski

Research output: Contribution to journalArticle

13 Citations (Scopus)

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. © 2006 ISI/BS.

Original languageEnglish
Pages (from-to)571-581
Number of pages11
JournalBernoulli
Volume12
Issue number4
DOIs
Publication statusPublished - Aug 2006

Keywords

  • Conditioning
  • Fluctuation theory
  • Lévy processes
  • Quasi-stationary distribution

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