On exponential functionals, harmonic potential measures and undershoots of subordinators

Larbi Alili; Wissem Jedidi; Víctor Rivero

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arXiv · 1310.4955

On exponential functionals, harmonic potential measures and undershoots of subordinators

Larbi Alili·Wissem Jedidi·Víctor Rivero

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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 function of an exponential functional $I$ and the so called remainder random variable $R$ associated to it. 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.

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Larbi Alili, Wissem Jedidi, Víctor Rivero. 2015-01-10. On exponential functionals, harmonic potential measures and undershoots of subordinators. https://arxiv.org/abs/1310.4955

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