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Lévy processes conditioned on having a large height process

Mathieu Richard (2013)

Annales de l'I.H.P. Probabilités et statistiques

In the present work, we consider spectrally positive Lévy processes ( X t , t 0 ) not drifting to + and we are interested in conditioning these processes to reach arbitrarily large heights (in the sense of the height process associated with X ) before hitting 0 . This way we obtain a new conditioning of Lévy processes to stay positive. The (honest) law x of this conditioned process (starting at x g t ; 0 ) is defined as a Doob h -transform via a martingale. For Lévy processes with infinite variation paths, this martingale...

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