Drift parameter estimation in the double mixed fractional Brownian model via solutions of Fredholm equations with singular kernels
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866914371946414080 |
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| author | Mishura, Yuliya Ralchenko, Kostiantyn Yakovliev, Mykyta |
| author_facet | Mishura, Yuliya Ralchenko, Kostiantyn Yakovliev, Mykyta |
| contents | We consider drift parameter estimation in a model driven by the sum of two independent fractional Brownian motions with different Hurst indices. Although the maximum likelihood estimator (MLE) for this model is known theoretically, its computation requires solving an operator equation involving fractional covariance operators. We develop an effective numerical method for approximating the solution of this equation by reformulating it as a Fredholm integral equation of the second kind with a weakly singular kernel. The resulting algorithm enables practical computation of the MLE. Numerical experiments illustrate the performance of the method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_05244 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Drift parameter estimation in the double mixed fractional Brownian model via solutions of Fredholm equations with singular kernels Mishura, Yuliya Ralchenko, Kostiantyn Yakovliev, Mykyta Probability 60G22, 62M09, 45B05, 65R20 We consider drift parameter estimation in a model driven by the sum of two independent fractional Brownian motions with different Hurst indices. Although the maximum likelihood estimator (MLE) for this model is known theoretically, its computation requires solving an operator equation involving fractional covariance operators. We develop an effective numerical method for approximating the solution of this equation by reformulating it as a Fredholm integral equation of the second kind with a weakly singular kernel. The resulting algorithm enables practical computation of the MLE. Numerical experiments illustrate the performance of the method. |
| title | Drift parameter estimation in the double mixed fractional Brownian model via solutions of Fredholm equations with singular kernels |
| topic | Probability 60G22, 62M09, 45B05, 65R20 |
| url | https://arxiv.org/abs/2603.05244 |