Stability for a functional differential equation in Hilbert space (Q2783485)
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scientific article; zbMATH DE number 1730459
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Stability for a functional differential equation in Hilbert space |
scientific article; zbMATH DE number 1730459 |
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21 April 2002
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signal detection
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Karhunen-Loéve approximations
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Gaussian noise detection
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0.99999976
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0.96854246
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0.95123637
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0.9509983
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0.94795483
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Stability for a functional differential equation in Hilbert space (English)
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The authors analyze the second order process \({x(t), t\in [0,T]}\), which is centered, mean square continuous and with a covariance function \(R(t,s)\). The approximations are derived using the method of Rayleigh-Ritz. The computation of an optimal linear estimation of a random signal with random noise interference and the detection of a centered Gaussian process in a deterministic signal are studied. An example is worked out when \(x(t)\) is a Wiener process in \([0,1]\).
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