Local properties of gaussian random fields on compact symmetric spaces and theorems of the Jackson-Bernstein type

• Date: 1999
• Main Authors: Malyarenko, A. A., Маляренко, А. А.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 1999
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/4583
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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,...