English

On the Laplace transform of perpetuities with thin tails

Probability 2009-12-23 v2

Abstract

We consider the random variables RR which are solutions of the distributional equation R=\cLMR+QR\overset{\cL}{=}MR+Q, where (Q,M)(Q,M) is independent of RR and \ABSM1\ABS{M}\leq 1. Goldie and Gr\"ubel showed that the tails of RR are no heavier than exponential. In this note we provide the exact lower and upper bounds of the domain of the Laplace transform of RR.

Keywords

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}
}