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On the entire moments of self-similar Markov processes and exponential functionals of Lévy processes


Bertoin, Jean; Yor, M (2002). On the entire moments of self-similar Markov processes and exponential functionals of Lévy processes. Universite Paul Sabatier. Faculte des Sciences. Annales: mathematiques, 11(1):33-45.

Abstract

We compute the positive entire moments of certain self-similar Markov processes evaluated at fixed time, and the negative entire moments of the exponential functional I of certain Lévy processes. When the Lévy process has no positive jumps, this determines the aforementioned distributions and yields several interesting identities in law. The case of the Poisson process yields yet another simple example showing that the log-normal distribution is moment-indeterminate.

Abstract

We compute the positive entire moments of certain self-similar Markov processes evaluated at fixed time, and the negative entire moments of the exponential functional I of certain Lévy processes. When the Lévy process has no positive jumps, this determines the aforementioned distributions and yields several interesting identities in law. The case of the Poisson process yields yet another simple example showing that the log-normal distribution is moment-indeterminate.

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Additional indexing

Item Type:Journal Article, not refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2002
Deposited On:03 Jul 2013 13:15
Last Modified:05 Apr 2016 16:51
Publisher:Universite de Toulouse III (Paul Sabatier)
ISSN:0240-2963
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.5802/afst.1016
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1986381
http://www.numdam.org/item?id=AFST_2002_6_11_1_33_0
http://www.numdam.org/numdam-bin/feuilleter?j=AFST

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