Computing Inverses of Stieltjes Transforms of Probability Measures
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916447995822080 |
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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 |