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arXiv · 2609.22952

Representation-free Densities of Ratios and Powers of Stable Variables

Nomvelo Karabo Sibisi·Sibusiso Sibisi
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Abstract

We derive representation-free densities of ratios and powers of the positive stable random variable given only its simple Laplace transform. This suffices to obtain Laplace/Stieltjes forward transforms of various random variable combinations. We state representation-free densities associated with occupation times (Lamperti, 1958) and Bessel process excursions (Bertoin et al., 2006) and their forward transforms. We also readily obtain simple representations of these and other densities using a known infinite series representation of the stable density.

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Nomvelo Karabo Sibisi, Sibusiso Sibisi. 2026-09-22. Representation-free Densities of Ratios and Powers of Stable Variables. https://arxiv.org/abs/2609.22952

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