Filtering of stochastic processes having periodically correlated increments
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866913229657079808 |
|---|---|
| author | Luz, Maksym Moklyachuk, Mikhail |
| author_facet | Luz, Maksym Moklyachuk, Mikhail |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_06396 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Filtering of stochastic processes having periodically correlated increments Luz, Maksym Moklyachuk, Mikhail Statistics Theory 60G10, 60G25, 60G35, 62M20, 62P20, 93E10, 93E11 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. |
| title | Filtering of stochastic processes having periodically correlated increments |
| topic | Statistics Theory 60G10, 60G25, 60G35, 62M20, 62P20, 93E10, 93E11 |
| url | https://arxiv.org/abs/2402.06396 |