Local properties of gaussian random fields on compact symmetric spaces and theorems of the Jackson-Bernstein type
We consider local properties of sample functions of Gaussian isotropic random fields on the compact Riemann symmetric spaces $\mathcal{M}$ of rank one. We give conditions under which the sample functions of a field almost surely possess logarithmic and power modulus of continuity. As a corollary,...
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| Datum: | 1999 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Ukrainisch Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
1999
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/4583 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | We consider local properties of sample functions of Gaussian isotropic random fields on the compact Riemann symmetric spaces $\mathcal{M}$ of rank one.
We give conditions under which the sample functions of a field almost surely possess logarithmic and power modulus of continuity.
As a corollary, we prove the Bernshtein-type theorem for optimal approximations of functions of this sort by harmonic polynomials in the metric of space $L_2(\mathcal{M})$.
We use the Jackson-Bernshtein-type theorems to obtain sufficient conditions of almost surely belonging of the sample functions of a field to classes of functions associated with Riesz and Cesaro means. |
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