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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
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: |
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| 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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