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On exponential functionals, harmonic potential measures and undershoots of subordinators

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Alili, Larbi, Jedidi, Wissem and Rivero, Victor (2014) On exponential functionals, harmonic potential measures and undershoots of subordinators. ALEA : Latin American Journal of Probability and Mathematical Statistics , 11 (2). pp. 711-735. ISSN 1980-0436.

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Official URL: http://alea.impa.br/articles/v11/11-33.pdf

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Abstract

We establish a link between the distribution of an exponential functional, I, and the undershoots of a subordinator, which is given in terms of the associated harmonic potential measure. This allows us to give a necessary and sufficient condition in terms of the Lévy measure for the exponential functional to be multiplicative infinitely divisible. We then provide a formula for the moment generating functions of log I and log R where R is the so-called remainder random variable associated to I. We provide a realization of the remainder random variable R as an infinite product involving independent last position random variables of the subordinator. Some properties of harmonic measures are obtained and some examples are provided.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > Science > Statistics
Library of Congress Subject Headings (LCSH): Exponential functions
Journal or Publication Title: ALEA : Latin American Journal of Probability and Mathematical Statistics
Publisher: Instituto Nacional de Matemática Pura e Aplicada
ISSN: 1980-0436
Official Date: 2014
Dates:
DateEvent
2014Published
Volume: 11
Number: 2
Page Range: pp. 711-735
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Funder: France. Agence nationale de la recherche (ANR), King Saud University, Riyadh, (KSA), Consejo Nacional de Ciencia y Tecnología (Mexico) [Mexican Council for Science and Technology] (CONACYT)
Grant number: ANR-09-Blan-0084-01 (ANR), MATH 01 (KSA), 134195 (CONACYT)
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