On distributional properties of perpetuities

Gerold Alsmeyer; Alex Iksanov; Uwe Roesler

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arXiv · 0803.3716

On distributional properties of perpetuities

Gerold Alsmeyer·Alex Iksanov·Uwe Roesler

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Abstract

We study probability distributions of convergent random series of a special structure, called perpetuities. By giving a new argument, we prove that such distributions are of pure type: degenerate, absolutely continuous, or continuously singular. We further provide necessary and sufficient criteria for the finiteness of $p$-moments, $p>0$ as well as exponential moments. In particular, a formula for the abscissa of convergence of the moment generating function is provided. The results are illustrated with a number of examples at the end of the article.

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Gerold Alsmeyer, Alex Iksanov, Uwe Roesler. 2008-03-26. On distributional properties of perpetuities. https://arxiv.org/abs/0803.3716

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