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## Filtering of Multidimensional Stationary Processes with Missing Observations

#### Oleksandr Masyutka [1] , Mikhail Moklyachuk [2] , Maria Sidei [3]

##### 20 46

The problem of the mean-square optimal linear estimation of linear functionals which depend on the unknown values of a multidimensional continuous time stationary stochastic process from observations of the process with a stationary noise is considered. Formulas for calculating the mean-square errors and the spectral characteristics of the optimal linear estimates of the functionals are derived under the condition of spectral certainty, where spectral densities of the signal and the noise processes are exactly known. The minimax (robust) method of estimation is applied in the case of spectral uncertainty, where spectral densities of the processes are not known exactly, while some sets of admissible spectral densities are given. Formulas that determine the least favorable spectral densities and minimax spectral characteristics of the optimal estimates are derived for some special sets of admissible spectral densities.
Minimax-Robust estimate, Least favourable spectral density
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Primary Language en Mathematics Articles Orcid: 0000-0002-7301-8813Author: Oleksandr MasyutkaInstitution: Taras Shevchenko National University of KyivCountry: Ukraine Orcid: 0000-0002-0605-0012Author: Mikhail Moklyachuk (Primary Author)Institution: Taras Shevchenko National University of KyivCountry: Ukraine Orcid: 0000-0003-1765-0969Author: Maria SideiInstitution: Taras Shevchenko National University of KyivCountry: Ukraine
 Bibtex @research article { ujma472929, journal = {Universal Journal of Mathematics and Applications}, issn = {2619-9653}, address = {Emrah Evren KARA}, year = {2019}, volume = {2}, pages = {24 - 32}, doi = {10.32323/ujma.472929}, title = {Filtering of Multidimensional Stationary Processes with Missing Observations}, key = {cite}, author = {Masyutka, Oleksandr and Moklyachuk, Mikhail and Sidei, Maria} } APA Masyutka, O , Moklyachuk, M , Sidei, M . (2019). Filtering of Multidimensional Stationary Processes with Missing Observations. Universal Journal of Mathematics and Applications, 2 (1), 24-32. DOI: 10.32323/ujma.472929 MLA Masyutka, O , Moklyachuk, M , Sidei, M . "Filtering of Multidimensional Stationary Processes with Missing Observations". Universal Journal of Mathematics and Applications 2 (2019): 24-32 Chicago Masyutka, O , Moklyachuk, M , Sidei, M . "Filtering of Multidimensional Stationary Processes with Missing Observations". Universal Journal of Mathematics and Applications 2 (2019): 24-32 RIS TY - JOUR T1 - Filtering of Multidimensional Stationary Processes with Missing Observations AU - Oleksandr Masyutka , Mikhail Moklyachuk , Maria Sidei Y1 - 2019 PY - 2019 N1 - doi: 10.32323/ujma.472929 DO - 10.32323/ujma.472929 T2 - Universal Journal of Mathematics and Applications JF - Journal JO - JOR SP - 24 EP - 32 VL - 2 IS - 1 SN - 2619-9653- M3 - doi: 10.32323/ujma.472929 UR - https://doi.org/10.32323/ujma.472929 Y2 - 2019 ER - EndNote %0 Universal Journal of Mathematics and Applications Filtering of Multidimensional Stationary Processes with Missing Observations %A Oleksandr Masyutka , Mikhail Moklyachuk , Maria Sidei %T Filtering of Multidimensional Stationary Processes with Missing Observations %D 2019 %J Universal Journal of Mathematics and Applications %P 2619-9653- %V 2 %N 1 %R doi: 10.32323/ujma.472929 %U 10.32323/ujma.472929 ISNAD Masyutka, Oleksandr , Moklyachuk, Mikhail , Sidei, Maria . "Filtering of Multidimensional Stationary Processes with Missing Observations". Universal Journal of Mathematics and Applications 2 / 1 (March 2019): 24-32. https://doi.org/10.32323/ujma.472929