Computing Inverses of Stieltjes Transforms of Probability Measures

Fuente: arXiv
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Autores principales: Chen, James, Olver, Sheehan
Formato: Preprint
Publicado: 2024
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author Chen, James
Olver, Sheehan
author_facet Chen, James
Olver, Sheehan
contents The Stieltjes (or sometimes called the Cauchy) transform is a fundamental object associated with probability measures, corresponding to the generating function of the moments. In certain applications such as free probability it is essential to compute the inverses of the Stieltjes transform, which might be multivalued. This paper establishes conditions bounding the number of inverses based on properties of the measure which can be combined with contour integral-based root finding algorithms to rigorously compute all inverses.
format Preprint
id arxiv_https___arxiv_org_abs_2410_16178
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Computing Inverses of Stieltjes Transforms of Probability Measures
Chen, James
Olver, Sheehan
Numerical Analysis
65E99, 65H05, 46L54
The Stieltjes (or sometimes called the Cauchy) transform is a fundamental object associated with probability measures, corresponding to the generating function of the moments. In certain applications such as free probability it is essential to compute the inverses of the Stieltjes transform, which might be multivalued. This paper establishes conditions bounding the number of inverses based on properties of the measure which can be combined with contour integral-based root finding algorithms to rigorously compute all inverses.
title Computing Inverses of Stieltjes Transforms of Probability Measures
topic Numerical Analysis
65E99, 65H05, 46L54
url https://arxiv.org/abs/2410.16178