Sharp inequalities involving multiplicative chaos sums
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866912753644470272 |
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| author | Karagulyan, Grigori A. |
| author_facet | Karagulyan, Grigori A. |
| contents | The present note is an essential addition to the author's arxiv paper arXiv:2001.01070, concerning general multiplicative systems of random variables. Using some lemmas and the methodology of \cite{Kar4}, we obtain a general extreme inequality, with corollaries involving Rademacher chaos sums and those analogues for multiplicative systems. In particular we prove that a system of functions generated by bounded products of a multiplicative system is a convergence system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_05431 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Sharp inequalities involving multiplicative chaos sums Karagulyan, Grigori A. Probability Classical Analysis and ODEs 42C05, 42C10, 42A55, 60G42, 60G48 The present note is an essential addition to the author's arxiv paper arXiv:2001.01070, concerning general multiplicative systems of random variables. Using some lemmas and the methodology of \cite{Kar4}, we obtain a general extreme inequality, with corollaries involving Rademacher chaos sums and those analogues for multiplicative systems. In particular we prove that a system of functions generated by bounded products of a multiplicative system is a convergence system. |
| title | Sharp inequalities involving multiplicative chaos sums |
| topic | Probability Classical Analysis and ODEs 42C05, 42C10, 42A55, 60G42, 60G48 |
| url | https://arxiv.org/abs/2212.05431 |