On exponential functionals, harmonic potential measures and undershoots of subordinators
Probability
2015-01-13 v4
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 L\'evy measure for the exponential functional to be multiplicative infinitely divisible. We then provide a formula for the moment generating function of an exponential functional and the so called remainder random variable associated to it. We provide a realization of the remainder random variable 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.
Cite
@article{arxiv.1310.4955,
title = {On exponential functionals, harmonic potential measures and undershoots of subordinators},
author = {Larbi Alili and Wissem Jedidi and Víctor Rivero},
journal= {arXiv preprint arXiv:1310.4955},
year = {2015}
}
Comments
24 pages