Hölder regularity and roughness: construction and examples
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866915257411174400 |
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| author | Bayraktar, Erhan Das, Purba Kim, Donghan |
| author_facet | Bayraktar, Erhan Das, Purba Kim, Donghan |
| contents | We study how to construct a stochastic process on a finite interval with given `roughness' and finite joint moments of marginal distributions. We first extend Ciesielski's isomorphism along a general sequence of partitions, and provide a characterization of Hölder regularity of a function in terms of its Schauder coefficients. Using this characterization we provide a better (pathwise) estimator of Hölder exponent. As an additional application, we construct fake (fractional) Brownian motions with some path properties and finite moments of marginal distributions same as (fractional) Brownian motions. These belong to non-Gaussian families of stochastic processes which are statistically difficult to distinguish from real (fractional) Brownian motions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_13794 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hölder regularity and roughness: construction and examples Bayraktar, Erhan Das, Purba Kim, Donghan Probability Applications 60H07, 60G22, 60G17, 62P05, 62M09, 42A16 We study how to construct a stochastic process on a finite interval with given `roughness' and finite joint moments of marginal distributions. We first extend Ciesielski's isomorphism along a general sequence of partitions, and provide a characterization of Hölder regularity of a function in terms of its Schauder coefficients. Using this characterization we provide a better (pathwise) estimator of Hölder exponent. As an additional application, we construct fake (fractional) Brownian motions with some path properties and finite moments of marginal distributions same as (fractional) Brownian motions. These belong to non-Gaussian families of stochastic processes which are statistically difficult to distinguish from real (fractional) Brownian motions. |
| title | Hölder regularity and roughness: construction and examples |
| topic | Probability Applications 60H07, 60G22, 60G17, 62P05, 62M09, 42A16 |
| url | https://arxiv.org/abs/2304.13794 |