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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.06806 |
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| _version_ | 1866929415138574336 |
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| author | Spodarev, Evgeny |
| author_facet | Spodarev, Evgeny |
| contents | This short note shows a limiting behavior of integrals of some centered antipersistent stationary infinitely divisible moving averages as the compact integration domain in $d\ge 1$ dimensions extends to the whole positive quadrant $\mathbb{R}^d_+$. Namely, the weak limit of their finite dimensional distributions is again a moving average with the same infinitely divisible purely jump integrator measure (i.e., possessing no Gaussian component), but with an integrated kernel function. The results apply equally to time series ($d=1$) as well as to random fields ($d>1$). Apart from the existence of the expectation, no moment assumptions on the moving average are imposed allowing it to have an infinite variance as e.g. in the case of $α$-stable moving averages with $α\in(1,2)$ . If the field is additionally square integrable, its covariance integrates to zero (hyperuniformity). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_06806 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Fubini-type limit theorem for the integrated hyperuniform infinitely divisible moving averages Spodarev, Evgeny Probability 60F05 This short note shows a limiting behavior of integrals of some centered antipersistent stationary infinitely divisible moving averages as the compact integration domain in $d\ge 1$ dimensions extends to the whole positive quadrant $\mathbb{R}^d_+$. Namely, the weak limit of their finite dimensional distributions is again a moving average with the same infinitely divisible purely jump integrator measure (i.e., possessing no Gaussian component), but with an integrated kernel function. The results apply equally to time series ($d=1$) as well as to random fields ($d>1$). Apart from the existence of the expectation, no moment assumptions on the moving average are imposed allowing it to have an infinite variance as e.g. in the case of $α$-stable moving averages with $α\in(1,2)$ . If the field is additionally square integrable, its covariance integrates to zero (hyperuniformity). |
| title | A Fubini-type limit theorem for the integrated hyperuniform infinitely divisible moving averages |
| topic | Probability 60F05 |
| url | https://arxiv.org/abs/2407.06806 |