Abelian and Tauberian theorems for random fields on two-point homogeneous spaces
Anatoliy Malyarenko · Theory of Probability and Mathematical Statistics · 2005
We consider centered mean-square continuous random fields for which the variance of increments between two points depends only on the distance between these points. Relations between the asymptotic behavior of the variance of increments near zero and the asymptotic behavior of the spectral measure of the field near infinity are investigated. We prove several Abelian and Tauberian theorems in terms of slowly varying functions.