Approximation of Nonhomogeneous Random Field from Local Averages

Abstract

In this article, we consider the extension of Shannon sampling series reconstruction theorem for nonhomogeneous random fields using local averages sampling, which helps improve certain earlier results. The upper bound of mean square truncation sampling approximation error is more precise, and we establish one approximation result in the almost sure sense.

Keywords:

• Average sampling
• local averages
• nonhomogeneous random field
• sampling theorem

Mathematics Subject Classification:

• 94A20
• 42C15
• 60G60

Acknowledgments

The authors would like to express their sincere gratitude to the anonymous referees and the editor for many valuable suggestions and insightful comments that helped to improve the article. Further acknowledgment is extended to Doctor Yumeng Song and Prof. Yong Zhang for their careful reading.

Additional information

Funding

This work was supported by the Shenzhen Sustainable Development Project (Grant No. KCXFZ20201221173013036) and the National Natural Science Foundation of China (Grant No. 61901294).