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arXiv · 0912.3232

On the Laplace transform of perpetuities with thin tails

Jean-Baptiste Bardet·Hélène Guerin·Florent Malrieu
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Abstract

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 Grübel 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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Jean-Baptiste Bardet, Hélène Guerin, Florent Malrieu. 2009-12-23. On the Laplace transform of perpetuities with thin tails. https://arxiv.org/abs/0912.3232

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