Sample behavior and laws of large numbers for Gaussian random elements.
Ergemlidze, Z., Shangua, A., Tarieladze, V. (2003)
Georgian Mathematical Journal
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Ergemlidze, Z., Shangua, A., Tarieladze, V. (2003)
Georgian Mathematical Journal
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Račkauskas, Alfredas, Suquet, Charles (2001)
Georgian Mathematical Journal
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Jiří Dvořák, Jiří Boldyš, Magdaléna Skopalová, Otakar Bělohlávek (2013)
Kybernetika
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This work presents new application of the random field theory in medical imaging. Results from both integral geometry and random field theory can be used to detect locations with significantly increased radiotracer uptake in images from positron emission tomography (PET). The assumptions needed to use these results are verified on a set of real and simulated phantom images. The proposed method of detecting activation (locations with increased radiotracer concentration) is used to quantify...
Rider, Brian, Virag, Balint (2007)
Electronic Journal of Probability [electronic only]
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Mamporia, B. (2000)
Georgian Mathematical Journal
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Seleši, Dora (2007)
Novi Sad Journal of Mathematics
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Viktor Beneš, Markéta Zikmundová (2014)
Kybernetika
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-statistics of spatial point processes given by a density with respect to a Poisson process are investigated. In the first half of the paper general relations are derived for the moments of the functionals using kernels from the Wiener-Itô chaos expansion. In the second half we obtain more explicit results for a system of -statistics of some parametric models in stochastic geometry. In the logarithmic form functionals are connected to Gibbs models. There is an inequality...
Martin Janžura (2014)
Kybernetika
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An efficient estimator for the expectation is constructed, where is a Gibbs random field, and is a local statistic, i. e. a functional depending on a finite number of coordinates. The estimator coincides with the empirical estimator under the conditions stated in Greenwood and Wefelmeyer [6], and covers the known special cases, namely the von Mises statistic for the i.i.d. underlying fields and the case of one-dimensional Markov chains.