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• W3119293823 endingPage "301" @default.
• W3119293823 startingPage "274" @default.
• W3119293823 abstract "Let (boldsymbol{f}) be a square-integrable, zero-mean, random vector with observable realizations in a Hilbert space (H), and let (boldsymbol{g}) be an associated square-integrable, zero-mean, random vector with realizations which are not observable in a Hilbert space (K). We seek an optimal filter in the form of a closed linear operator (X) acting on the observable realizations of a proximate vector (boldsymbol{f}_{epsilon} approx boldsymbol{f}) that provides the best estimate (widehat{boldsymbol{g}}_{epsilon} = X! boldsymbol{f}_{epsilon}) of the vector (boldsymbol{g}). We assume the required covariance operators are known. The results are illustrated with a typical example. doi:10.1017/S1446181120000188" @default.
• W3119293823 created "2021-01-18" @default.
• W3119293823 creator A5021819105 @default.
• W3119293823 creator A5027557193 @default.
• W3119293823 date "2021-02-04" @default.
• W3119293823 modified "2023-09-27" @default.
• W3119293823 title "An optimal linear filter for estimation of random functions in Hilbert space" @default.
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• W3119293823 doi "https://doi.org/10.21914/anziamj.v62.15576" @default.
• W3119293823 hasPublicationYear "2021" @default.
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