Levy processes with finite variance conditioned to avoid an interval

Leif Doring, Alexander R. Watson, Philip Weissmann

    Research output: Contribution to journalArticlepeer-review


    Conditioning Markov processes to avoid a set is a classical problem that has been studied in many settings. In the present article we study the question if a Lévy process can be conditioned to avoid an interval and, if so, the path behavior of the conditioned process. For Lévy processes with finite second moments we show that conditioning is possible and identify the conditioned process as an h-transform of the original killed process. The h-transform is explicit in terms of successive overshoot distributions and is used to prove that the conditioned process diverges to +∞ and −∞ with positive probabilities.
    Original languageEnglish
    JournalElectronic Journal of Probability
    Publication statusPublished - 5 Jun 2019


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