Evgeny Spodarev, Elena Shmileva, Stefan Roth
Published 2013-06-26Version 1
We introduce basic statistical methods for the extrapolation of stationary random fields. For square integrable fields, we set out basics of the kriging extrapolation techniques. For (non--Gaussian) stable fields, which are known to be heavy tailed, we describe further extrapolation methods and discuss their properties. Two of them can be seen as direct generalizations of kriging.
Comments: 52 pages, 25 figures. This is a review article, though Section 4 of the article contains new results on the weak consistency of the extrapolation methods as well as new extrapolation methods for $\alpha$-stable fields with $0<\alpha\leq 1$
Stationary random fields with linear regressions
Limit theorems for excursion sets of stationary random fields
A central limit theorem for stationary random fields
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