On almost everywhere convergence of the Riesz averages of homogeneous random fields

V. F. Gaposhkin

Moscow State University of Railway Communications

Abstract: Weighted averages are studied for wide-sense homogeneous random fields in $\mathbb R^k$ with spherically symmetric weights. A representation obtained for these averages permits us to prove along with a criterion for almost everywhere summability of homogeneous random fields a number of corollaries as well.

Keywords: wide-sense homogeneous random fields, spectral measure of a field, weighted averages, correlation function, almost everywhere summability, logarithmic Riesz averages.

Received: 11.01.1996

DOI: 10.4213/tvp1944

 English version: Theory of Probability and its Applications, 1998, 42:3, 405–415

Bibliographic databases:

• 
• 
•