Central limit theorem under the Dedecker-Rio condition in some Banach spaces
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909249968275456 |
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| author | Bigot, Aurélie |
| author_facet | Bigot, Aurélie |
| contents | We extend the central limit theorem under the Dedecker-Rio condition to adapted stationary and ergodic sequences of random variables taking values in a class of smooth Banach spaces. This result applies to the case of random variables taking values in $L^p(μ)$, with $2 \leq p < \infty$ and $μ$ a $σ$-finite real measure. As an application we give a sufficient condition for empirical processes indexed by Sobolev balls to satisfy the central limit theorem, and discuss about the optimality of these conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_01564 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Central limit theorem under the Dedecker-Rio condition in some Banach spaces Bigot, Aurélie Probability We extend the central limit theorem under the Dedecker-Rio condition to adapted stationary and ergodic sequences of random variables taking values in a class of smooth Banach spaces. This result applies to the case of random variables taking values in $L^p(μ)$, with $2 \leq p < \infty$ and $μ$ a $σ$-finite real measure. As an application we give a sufficient condition for empirical processes indexed by Sobolev balls to satisfy the central limit theorem, and discuss about the optimality of these conditions. |
| title | Central limit theorem under the Dedecker-Rio condition in some Banach spaces |
| topic | Probability |
| url | https://arxiv.org/abs/2307.01564 |