On the Laplace transform of perpetuities with thin tails

Details On the Laplace transform of perpetuities with thin tails On the Laplace transform of perpetuities with thin tails

2009-12-16

arxiv.org/abs/0912.3232v2

Mathematics

Probability

Scientific paper

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

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