This book presents an overview of reproducing kernel Hilbert, Sobolev, and H lder spaces. Unlike most related books, this one brings together the two perspectives of geostatistics and reproducing kernel Hilbert spaces. It begins with second-order random fields defined over Hilbert spaces and then progresses to applications to space, space-time random fields, vector-valued random fields, functional geostatistics, and extreme-valued random fields. The book includes real-world examples and case studies that illustrate data analysis and simulation. All examples are implemented with R packages.
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