تقرير
Filtering of stochastic processes having periodically correlated increments
| العنوان: | Filtering of stochastic processes having periodically correlated increments |
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| المؤلفون: | Luz, Maksym, Moklyachuk, Mikhail |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics Statistics |
| مصطلحات موضوعية: | Mathematics - Statistics Theory, 60G10, 60G25, 60G35, 62M20, 62P20, 93E10, 93E11 |
| الوصف: | We deal with the problem of the mean square optimal estimation of linear transformations of the unobserved values of a continuous time stochastic process with periodically correlated increments. Estimates are based on observations of the process with a continuous time stochastic noise process which is periodically correlated increments as well. To solve the problem, we transform the processes to infinite dimensional vector valued stationary sequences. We obtain formulas for calculating the mean square errors and the spectral characteristics of the optimal estimates of the transformations. Formulas determining the least favorable spectral densities and the minimax-robust spectral characteristics of the optimal estimates of transformations are derived. Comment: arXiv admin note: substantial text overlap with arXiv:2401.08642, arXiv:2304.12220; text overlap with arXiv:2307.02676, arXiv:2304.13683 |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2402.06396 |
| رقم الأكسشن: | edsarx.2402.06396 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |