On Distributional Properties of Perpetuities

Gerold Alsmeyer (), Alex Iksanov () and Uwe Rösler ()
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Gerold Alsmeyer: Westfälische Wilhelms-Universität Münster
Alex Iksanov: National T. Shevchenko University
Uwe Rösler: Christian-Albrechts-Universität zu Kiel

Journal of Theoretical Probability, 2009, vol. 22, issue 3, 666-682

Abstract: 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.

Keywords: Perpetuity; Continuity of distribution; Atom; Moment; Exponential moment; Abscissa of convergence; 60E99; 60G50 (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10959-008-0156-8

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