Convolution powers of unbounded measures on the positive half-line
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913304914427904 |
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| author | Buraczewski, Dariusz Iksanov, Alexander Marynych, Alexander |
| author_facet | Buraczewski, Dariusz Iksanov, Alexander Marynych, Alexander |
| contents | For a right-continuous nondecreasing and unbounded function $V$ of at most exponential growth, which vanishes on the negative halfline, we investigate the asymptotic behavior of the Lebesgue-Stieltjes convolution powers $V^{\ast(j)}(t)$ as both $j$ and $t$ tend to infinity. We obtain a comprehensive asymptotic formula for $V^{\ast(j)}(t)$, which is valid across different regimes of simultaneous growth of $j$ and $t$. Our main technical tool is an exponential change of measure, which is a standard technique in the large deviations theory. Various applications of our result are given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_04955 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Convolution powers of unbounded measures on the positive half-line Buraczewski, Dariusz Iksanov, Alexander Marynych, Alexander Probability Classical Analysis and ODEs Primary: 60F10, Secondary: 44A35, 60J80 For a right-continuous nondecreasing and unbounded function $V$ of at most exponential growth, which vanishes on the negative halfline, we investigate the asymptotic behavior of the Lebesgue-Stieltjes convolution powers $V^{\ast(j)}(t)$ as both $j$ and $t$ tend to infinity. We obtain a comprehensive asymptotic formula for $V^{\ast(j)}(t)$, which is valid across different regimes of simultaneous growth of $j$ and $t$. Our main technical tool is an exponential change of measure, which is a standard technique in the large deviations theory. Various applications of our result are given. |
| title | Convolution powers of unbounded measures on the positive half-line |
| topic | Probability Classical Analysis and ODEs Primary: 60F10, Secondary: 44A35, 60J80 |
| url | https://arxiv.org/abs/2404.04955 |