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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Datum:2007
1. Verfasser: Moklyachuk, M.
Format: Artikel
Sprache:English
Veröffentlicht: Інститут математики НАН України 2007
Online Zugang: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
Zitieren: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.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-4518
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
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Prediction problem for random fields on groups
spellingShingle Prediction problem for random fields on groups
Moklyachuk, M.
title_short 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_sort prediction problem for random fields on groups
author Moklyachuk, M.
author_facet Moklyachuk, M.
publishDate 2007
language English
publisher Інститут математики НАН України
format Article
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.
issn 0321-3900
url https://nasplib.isofts.kiev.ua/handle/123456789/4518
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.
work_keys_str_mv AT moklyachukm predictionproblemforrandomfieldsongroups
first_indexed 2025-12-02T00:42:16Z
last_indexed 2025-12-02T00:42:16Z
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