On distributional properties of perpetuities

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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.
to appear in Journal of Theoretical Probability

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Probability, 60E99; 60G50

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http://salesiana.dossiersoluciones.com/handle/123456789/157455

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0803.3716
 http://arxiv.org/abs/0803.3716

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arXiv