PreprintCC BY 4.0arXiv
Representation-free Densities of Ratios and Powers of Stable Variables
Abstract
We derive representation-free densities of ratios of the positive stable random variable and obtain their Laplace/Stieltjes transforms. We state representation-free densities of occupation times (Lamperti, 1958) and Bessel process excursions (Bertoin et al., 2006) and their transforms. We also obtain simple representations of these and other densities using a known infinite series representation of the stable density.
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BibTeX
@misc{sibisi2026representationfree,
title = {{Representation-free Densities of Ratios and Powers of Stable Variables}},
author = {Nomvelo Karabo Sibisi and Sibusiso Sibisi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.22952},
eprint = {2609.22952},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.22952},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Representation-free Densities of Ratios and Powers of Stable Variables
AU - Nomvelo Karabo Sibisi
AU - Sibusiso Sibisi
PY - 2026
DA - 2026/10/03
PB - arXiv
DO - 10.48550/arxiv.2609.22952
UR - https://arxiv.org/abs/2609.22952
AB - We derive representation-free densities of ratios of the positive stable random variable and obtain their Laplace/Stieltjes transforms. We state representation-free densities of occupation times (Lamperti, 1958) and Bessel process excursions (Bertoin et al., 2006) and their transforms. We also obtain simple representations of these and other densities using a known infinite series representation of the stable density.
ER -