A Koopman-Takens theorem: linear least squares prediction of nonlinear time series (Q6536643)
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scientific article; zbMATH DE number 7846282
| Language | Label | Description | Also known as |
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| English | A Koopman-Takens theorem: linear least squares prediction of nonlinear time series |
scientific article; zbMATH DE number 7846282 |
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A Koopman-Takens theorem: linear least squares prediction of nonlinear time series (English)
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13 May 2024
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\textit{F. Takens} [Lect. Notes Math. 898, 366--381 (1981; Zbl 0513.58032)] showed that nonlinear mappings of time-delayed observations on a deterministic system allow exact predictability for a large (open and dense in a suitable topology) class of dynamical systems. Here the so-called forecast problem for invertible measure-preserving systems and methods from ergodic theory are used to show a similar result for linear least-squares filter in the infinite-delay limit.
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Wiener filters
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Koopman operators
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Takens' theorem
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