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Pré-Publication, Document De Travail Année : 2004

Markov property of monotone Lévy processes

Uwe Franz
Naofumi Muraki
  • Fonction : Auteur

Résumé

Monotone Lévy processes with additive increments are defined and studied. It is shown that these processes have a natural Markov structure and their Markov transition semigroups are characterized using the monotone Lévy-Khintchine formula. Monotone Lévy processes turn out to be related to classical Lévy processes via Attal's ``remarkable transformation.'' A monotone analogue of the family of exponential martingales associated to a classical Lévy process is also defined.

Dates et versions

hal-00470214 , version 1 (05-04-2010)

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Uwe Franz, Naofumi Muraki. Markov property of monotone Lévy processes. 2004. ⟨hal-00470214⟩
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