A law of the iterated logarithm for the number of blocks in regenerative compositions generated by gamma-like subordinators
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910483460653056 |
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| author | Iksanov, Alexander Jedidi, Wissem |
| author_facet | Iksanov, Alexander Jedidi, Wissem |
| contents | The points of the closed range of a drift-free subordinator with no killing are used for separating into blocks the elements of a sample of size $n$ from the standard exponential distribution. This gives rise to a random composition of $n$. Assuming that the subordinator has the Lévy measure, which behaves near zero like the gamma subordinator, we prove a law of the iterated logarithm for the number of blocks in the composition as $n$ tends to infinity. Along the way we prove a law of the iterated logarithm for the Lebesgue convolution of a standard Brownian motion and a deterministic regularly varying function. This result may be of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_08370 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A law of the iterated logarithm for the number of blocks in regenerative compositions generated by gamma-like subordinators Iksanov, Alexander Jedidi, Wissem Probability The points of the closed range of a drift-free subordinator with no killing are used for separating into blocks the elements of a sample of size $n$ from the standard exponential distribution. This gives rise to a random composition of $n$. Assuming that the subordinator has the Lévy measure, which behaves near zero like the gamma subordinator, we prove a law of the iterated logarithm for the number of blocks in the composition as $n$ tends to infinity. Along the way we prove a law of the iterated logarithm for the Lebesgue convolution of a standard Brownian motion and a deterministic regularly varying function. This result may be of independent interest. |
| title | A law of the iterated logarithm for the number of blocks in regenerative compositions generated by gamma-like subordinators |
| topic | Probability |
| url | https://arxiv.org/abs/2406.08370 |