Infinite Dimensional Multifractal Analysis of the Wiener measure
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914328232329216 |
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| author | Fan, Aihua Helfter, Mathieu |
| author_facet | Fan, Aihua Helfter, Mathieu |
| contents | We present a multifractal formalism for measures on infinite dimensional metric spaces, in terms of scales instead of dimensions in the classical multifractal analysis. We prove a multifractal formalism with a suitable scaling, called order, for the Wiener measure, which is the probability law of the standard Brownian motion. We also prove the fundamental Frostman Lemma on a large class of Polish spaces, for which the increasing sets lemma holds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_06984 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Infinite Dimensional Multifractal Analysis of the Wiener measure Fan, Aihua Helfter, Mathieu Probability 60J65, 28A80 We present a multifractal formalism for measures on infinite dimensional metric spaces, in terms of scales instead of dimensions in the classical multifractal analysis. We prove a multifractal formalism with a suitable scaling, called order, for the Wiener measure, which is the probability law of the standard Brownian motion. We also prove the fundamental Frostman Lemma on a large class of Polish spaces, for which the increasing sets lemma holds. |
| title | Infinite Dimensional Multifractal Analysis of the Wiener measure |
| topic | Probability 60J65, 28A80 |
| url | https://arxiv.org/abs/2512.06984 |