On Construction, Properties and Simulation of Haar-Based Multifractional Processes
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866910867307626496 |
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| author | Ayache, Antoine Olenko, Andriy Samarakoon, Nemini |
| author_facet | Ayache, Antoine Olenko, Andriy Samarakoon, Nemini |
| contents | Multifractional processes extend the concept of fractional Brownian motion by replacing the constant Hurst parameter with a time-varying Hurst function. This extension allows for modulation of the roughness of sample paths over time. The paper introduces a new class of multifractional processes, the Gaussian Haar-based multifractional processes (GHBMP), which is based on the Haar wavelet series representations. The resulting processes cover a significantly broader set of Hurst functions compared to the existing literature, enhancing their suitability for both practical applications and theoretical studies. The theoretical properties of these processes are investigated. Simulation studies conducted for various Hurst functions validate the proposed model and demonstrate its applicability, even for Hurst functions exhibiting discontinuous behaviour. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_07286 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Construction, Properties and Simulation of Haar-Based Multifractional Processes Ayache, Antoine Olenko, Andriy Samarakoon, Nemini Probability 60G22, 60G15, 62M99, 65C20 Multifractional processes extend the concept of fractional Brownian motion by replacing the constant Hurst parameter with a time-varying Hurst function. This extension allows for modulation of the roughness of sample paths over time. The paper introduces a new class of multifractional processes, the Gaussian Haar-based multifractional processes (GHBMP), which is based on the Haar wavelet series representations. The resulting processes cover a significantly broader set of Hurst functions compared to the existing literature, enhancing their suitability for both practical applications and theoretical studies. The theoretical properties of these processes are investigated. Simulation studies conducted for various Hurst functions validate the proposed model and demonstrate its applicability, even for Hurst functions exhibiting discontinuous behaviour. |
| title | On Construction, Properties and Simulation of Haar-Based Multifractional Processes |
| topic | Probability 60G22, 60G15, 62M99, 65C20 |
| url | https://arxiv.org/abs/2503.07286 |