Moments of last exit times for Lévy processes
Ken-Iti Sato, Toshiro Watanabe (2004)
Annales de l'I.H.P. Probabilités et statistiques
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Ken-Iti Sato, Toshiro Watanabe (2004)
Annales de l'I.H.P. Probabilités et statistiques
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A. E. Kyprianou, P. Patie (2011)
Annales de l'I.H.P. Probabilités et statistiques
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The aim of this note is to give a straightforward proof of a general version of the Ciesielski–Taylor identity for positive self-similar Markov processes of the spectrally negative type which umbrellas all previously known Ciesielski–Taylor identities within the latter class. The approach makes use of three fundamental features. Firstly, a new transformation which maps a subset of the family of Laplace exponents of spectrally negative Lévy processes into itself. Secondly, some classical...
Anthony G. Pakes (1996)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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Kouji Yano, Yuko Yano, Marc Yor (2010)
Annales de l'I.H.P. Probabilités et statistiques
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Penalisation involving the one-sided supremum for a stable Lévy process with index ∈(0, 2] is studied. We introduce the analogue of Azéma–Yor martingales for a stable Lévy process and give the law of the overall supremum under the penalised measure.
Gennady Samorodnitsky (2006)
Annales de la faculté des sciences de Toulouse Mathématiques
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This paper is a survey of both classical and new results and ideas on long memory, scaling and self-similarity, both in the light-tailed and heavy-tailed cases.
Jan Rosiński, Jennifer L. Sinclair (2010)
Banach Center Publications
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This work introduces the class of generalized tempered stable processes which encompass variations on tempered stable processes that have been introduced in the field, including "modified tempered stable processes", "layered stable processes", and "Lamperti stable processes". Short and long time behavior of GTS Lévy processes is characterized and the absolute continuity of GTS processes with respect to the underlying stable processes is established. Series representations of GTS Lévy...