On distributional properties of perpetuities

Details On distributional properties of perpetuities On distributional properties of perpetuities

2008-03-26

arxiv.org/abs/0803.3716v1

Mathematics

Probability

to appear in Journal of Theoretical Probability

Scientific paper

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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