Prediction problem for random fields on groups
The problem considered is the problem of optimal linear estimation of the functional Aξ = ∑↑∞↓j=0 ∫↓G a(g, j)ξ(g, j)dg which depends on the unknown values of a homogeneous random field ξ(g, j) on the group G × Z from observations of the field ξ(g, j) + η(g, j) for (g, j) belongs G×{−1,−2, . . .}, wher...
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| Дата: | 2007 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2007
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/4518 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Prediction problem for random fields on groups / M. Moklyachuk // Theory of Stochastic Processes. — 2007. — Т. 13 (29), № 4. — С. 148–162. — Бібліогр.: 20 назв.— англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862654505070362624 |
|---|---|
| author | Moklyachuk, M. |
| author_facet | Moklyachuk, M. |
| citation_txt | Prediction problem for random fields on groups / M. Moklyachuk // Theory of Stochastic Processes. — 2007. — Т. 13 (29), № 4. — С. 148–162. — Бібліогр.: 20 назв.— англ. |
| collection | DSpace DC |
| description | The problem considered is the problem of optimal linear estimation of the functional Aξ = ∑↑∞↓j=0 ∫↓G a(g, j)ξ(g, j)dg which depends on the unknown values of a homogeneous random field ξ(g, j) on the group G × Z from observations of the field ξ(g, j) + η(g, j) for (g, j) belongs G×{−1,−2, . . .}, where η(g, j) is an uncorrelated with ξ(g, j) homogeneous random field ξ(g, j) on the group G×Z. Formulas are proposed for calculation the mean square error and spectral characteristics of the optimal linear estimate in the case where spectral densities of the fields are known. The least favorable spectral densities and the minimax spectral characteristics of the optimal estimate of the functional are found for some classes of spectral densities.
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| first_indexed | 2025-12-02T00:42:16Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-4518 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0321-3900 |
| language | English |
| last_indexed | 2025-12-02T00:42:16Z |
| publishDate | 2007 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Moklyachuk, M. 2009-11-24T15:31:52Z 2009-11-24T15:31:52Z 2007 Prediction problem for random fields on groups / M. Moklyachuk // Theory of Stochastic Processes. — 2007. — Т. 13 (29), № 4. — С. 148–162. — Бібліогр.: 20 назв.— англ. 0321-3900 https://nasplib.isofts.kiev.ua/handle/123456789/4518 The problem considered is the problem of optimal linear estimation of the functional Aξ = ∑↑∞↓j=0 ∫↓G a(g, j)ξ(g, j)dg which depends on the unknown values of a homogeneous random field ξ(g, j) on the group G × Z from observations of the field ξ(g, j) + η(g, j) for (g, j) belongs G×{−1,−2, . . .}, where η(g, j) is an uncorrelated with ξ(g, j) homogeneous random field ξ(g, j) on the group G×Z. Formulas are proposed for calculation the mean square error and spectral characteristics of the optimal linear estimate in the case where spectral densities of the fields are known. The least favorable spectral densities and the minimax spectral characteristics of the optimal estimate of the functional are found for some classes of spectral densities. en Інститут математики НАН України Prediction problem for random fields on groups Article published earlier |
| spellingShingle | Prediction problem for random fields on groups Moklyachuk, M. |
| title | Prediction problem for random fields on groups |
| title_full | Prediction problem for random fields on groups |
| title_fullStr | Prediction problem for random fields on groups |
| title_full_unstemmed | Prediction problem for random fields on groups |
| title_short | Prediction problem for random fields on groups |
| title_sort | prediction problem for random fields on groups |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/4518 |
| work_keys_str_mv | AT moklyachukm predictionproblemforrandomfieldsongroups |