Sample Path Properties of the Fractional Wiener--Weierstrass Bridge
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916473211977728 |
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| author | Schied, Alexander Zhang, Zhenyuan |
| author_facet | Schied, Alexander Zhang, Zhenyuan |
| contents | Fractional Wiener--Weierstrass bridges are a class of Gaussian processes that arise from replacing the trigonometric function in the construction of classical Weierstrass functions by a fractional Brownian bridge. We investigate the sample path properties of such processes, including local and uniform moduli of continuity, $Φ$-variation, Hausdorff dimension, and location of the maximum. Our analysis relies heavily on upper and lower bounds of fractional integrals, where we establish a novel improvement of the classical Hardy--Littlewood inequality for fractional integrals of a special class of step functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_05204 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sample Path Properties of the Fractional Wiener--Weierstrass Bridge Schied, Alexander Zhang, Zhenyuan Probability Fractional Wiener--Weierstrass bridges are a class of Gaussian processes that arise from replacing the trigonometric function in the construction of classical Weierstrass functions by a fractional Brownian bridge. We investigate the sample path properties of such processes, including local and uniform moduli of continuity, $Φ$-variation, Hausdorff dimension, and location of the maximum. Our analysis relies heavily on upper and lower bounds of fractional integrals, where we establish a novel improvement of the classical Hardy--Littlewood inequality for fractional integrals of a special class of step functions. |
| title | Sample Path Properties of the Fractional Wiener--Weierstrass Bridge |
| topic | Probability |
| url | https://arxiv.org/abs/2411.05204 |