Limit theorems for random Dirichlet series: boundary case
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913571308306432 |
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| author | Iksanov, Alexander Kostohryz, Ruslan |
| author_facet | Iksanov, Alexander Kostohryz, Ruslan |
| contents | Buraczewski et al (2023) proved a functional limit theorem (FLT) and a law of the iterated logarithm (LIL) for a random Dirichlet series $\sum_{k\geq 2}(\log k)^αk^{-1/2-s}η_k$ as $s\to 0+$, where $α>-1/2$ and $η_1$, $η_2,\ldots$ are independent identically distributed random variables with zero mean and finite variance. We prove a FLT and a LIL in a boundary case $α=-1/2$. The boundary case is more demanding technically than the case $α>-1/2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_02362 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Limit theorems for random Dirichlet series: boundary case Iksanov, Alexander Kostohryz, Ruslan Probability Buraczewski et al (2023) proved a functional limit theorem (FLT) and a law of the iterated logarithm (LIL) for a random Dirichlet series $\sum_{k\geq 2}(\log k)^αk^{-1/2-s}η_k$ as $s\to 0+$, where $α>-1/2$ and $η_1$, $η_2,\ldots$ are independent identically distributed random variables with zero mean and finite variance. We prove a FLT and a LIL in a boundary case $α=-1/2$. The boundary case is more demanding technically than the case $α>-1/2$. |
| title | Limit theorems for random Dirichlet series: boundary case |
| topic | Probability |
| url | https://arxiv.org/abs/2411.02362 |