Spectral theory for random closed sets and estimating the covariance via frequency space
A spectral theory for stationary random closed sets is developed and provided with a sound mathematical basis. The definition and a proof of the existence of the Bartlett spectrum of a stationary random closed set as well as the proof of a Wiener-Khinchin theorem for the power spectrum are used to t...
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| Veröffentlicht in: | Advances in applied probability 2003-09, Vol.35 (3), p.603-613 |
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| container_end_page | 613 |
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| container_issue | 3 |
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| container_title | Advances in applied probability |
| container_volume | 35 |
| creator | Koch, Karsten Ohser, Joachim Schladitz, Katja |
| description | A spectral theory for stationary random closed sets is developed and provided with a sound mathematical basis. The definition and a proof of the existence of the Bartlett spectrum of a stationary random closed set as well as the proof of a Wiener-Khinchin theorem for the power spectrum are used to two ends. First, well-known second-order characteristics like the covariance can be estimated faster than usual via frequency space. Second, the Bartlett spectrum and the power spectrum can be used as second-order characteristics in frequency space. Examples show that in some cases information about the random closed set is easier to obtain from these characteristics in frequency space than from their real-world counterparts. |
| doi_str_mv | 10.1239/aap/1059486820 |
| format | Article |
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The definition and a proof of the existence of the Bartlett spectrum of a stationary random closed set as well as the proof of a Wiener-Khinchin theorem for the power spectrum are used to two ends. First, well-known second-order characteristics like the covariance can be estimated faster than usual via frequency space. Second, the Bartlett spectrum and the power spectrum can be used as second-order characteristics in frequency space. 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| ispartof | Advances in applied probability, 2003-09, Vol.35 (3), p.603-613 |
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| language | eng |
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| source | JSTOR |
| subjects | 42B10 60D05 62G05 62M40 Bartlett spectrum Covariance Density estimation fast Fourier transform Fast Fourier transformations Fourier transformations Geometry Image analysis Mathematical models power spectrum Probability Random set Random variables Rotational spectra Sine function Spectral energy distribution Spectroscopy Spectrum analysis Stochastic Geometry and Statistical Applications Studies Variance analysis |
| title | Spectral theory for random closed sets and estimating the covariance via frequency space |
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