{"ID":2847053,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.00990","arxiv_id":"2511.00990","title":"Filtering of periodically correlated processes","abstract":"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.","short_abstract":"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...","url_abs":"https://arxiv.org/abs/2511.00990","url_pdf":"https://arxiv.org/pdf/2511.00990v2","authors":"[\"Iryna Dubovets'ka\",\"Mykhailo Moklyachuk\"]","published":"2025-11-02T16:04:06Z","proceeding":"math.ST","tasks":"[\"math.ST\"]","methods":"[]","has_code":false}