On the Laplace transform of perpetuities with thin tails
Probability
2009-12-23 v2
Abstract
We consider the random variables which are solutions of the distributional equation , where is independent of and . Goldie and Gr\"ubel showed that the tails of are no heavier than exponential. In this note we provide the exact lower and upper bounds of the domain of the Laplace transform of .
Cite
@article{arxiv.0912.3232,
title = {On the Laplace transform of perpetuities with thin tails},
author = {Jean-Baptiste Bardet and Hélène Guerin and Florent Malrieu},
journal= {arXiv preprint arXiv:0912.3232},
year = {2009}
}