Velikoivanenko, A. I. Some properties of realizations of processes and fields of Pólya type. (English. Russian original) Zbl 0738.60030 Theory Probab. Math. Stat. 43, 41-50 (1991); translation from Teor. Veroyatn. Mat. Stat., Kiev 43, 37-47 (1990). Summary: Local properties are considered for realizations of processes and fields and correlation functions satisfying the conditions of the Pólya theorem. It is shown that such processes and fields are nowhere differentiable almost surely. Criteria are obtained for sample continuity of the processes and fields, and their Lipschitz properties and exact moduli of continuity are studied. MSC: 60G17 Sample path properties 60G60 Random fields 60G10 Stationary stochastic processes 60G15 Gaussian processes Keywords:local properties; correlation functions; sample continuity; Lipschitz properties; moduli of continuity PDFBibTeX XMLCite \textit{A. I. Velikoivanenko}, Theory Probab. Math. Stat. 43, 41--50 (1990; Zbl 0738.60030); translation from Teor. Veroyatn. Mat. Stat., Kiev 43, 37--47 (1990)