Approximation of homogeneous random field from local averages
Shuo Zhang, Zhanjie Song, Ying Li · Communication in Statistics- Theory and Methods · 2016
Based on the Shannon sampling theorem of multivariate functions, the upper bound of approximated error of homogeneous random field by local averages in the mean square sense is established. The main result is that the approximation of weak sense stochastic process from local averages is extended to the case of random field. It is expected that one can obtain more precise local average sampling in oceanography, meteorology, geology with this theory.