Approximation of homogeneous random field from local averages

ABSTRACT

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.

KEYWORDS:

• Average sampling
• homogeneous random field
• local averages
• sampling theorem.

MATHEMATICS SUBJECT CLASSIFICATION:

• 60G60
• 42C15
• 94A20

Funding

This work was supported partially by the National Natural Science Foundation of China(Grant No. 61379014). Further acknowledgement is extended to the reviews for their insightful comments which greatly improved the paper.