Filtering of periodically correlated processes
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912718370373632 |
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| author | Dubovets'ka, Iryna Moklyachuk, Mykhailo |
| author_facet | Dubovets'ka, Iryna Moklyachuk, Mykhailo |
| contents | The problem of optimal linear estimation of a linear functional depending on the unknown values of periodically correlated stochastic process from observations of the process with additive noise is considered. Formulas for calculating the mean square error and the spectral characteristic of the optimal linear estimate of the functional are proposed in the case where spectral densities are exactly known. Formulas that determine the least favorable spectral densities and the minimax (robust) spectral characteristics are proposed for a given class of admissible spectral densities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_00990 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Filtering of periodically correlated processes Dubovets'ka, Iryna Moklyachuk, Mykhailo Statistics Theory 60G25, 60G35, 62M20, 93E10 The problem of optimal linear estimation of a linear functional depending on the unknown values of periodically correlated stochastic process from observations of the process with additive noise is considered. Formulas for calculating the mean square error and the spectral characteristic of the optimal linear estimate of the functional are proposed in the case where spectral densities are exactly known. Formulas that determine the least favorable spectral densities and the minimax (robust) spectral characteristics are proposed for a given class of admissible spectral densities. |
| title | Filtering of periodically correlated processes |
| topic | Statistics Theory 60G25, 60G35, 62M20, 93E10 |
| url | https://arxiv.org/abs/2511.00990 |