On distributional properties of perpetuities

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.

to appear in Journal of Theoretical Probability

References in corpus (1)

• A log-type moment result for perpetuities and its application to martingales in supercritical branching random walks

Cited by in corpus (1)

• On a random recursion related to absorption times of death Markov chains