On the Existence of Mosaic and Indicator Random Fields with Spherical,Circular, and Triangular Variograms |
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| Authors: | Xavier Emery |
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| Institution: | (1) Spatial Ecology and Epidemiology Group, University of Oxford, South Park Road, Oxford, OX1 3PS, UK;(2) School of Geography, University of Southampton, Highfield, Southampton, S017 1BJ, UK;(3) IRSA-CNR, National Research Council, via F. De Blasio 5, 70123 Bari, Italy |
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| Abstract: | This paper focuses on two specific families of stationary random fields (namely, mosaic and indicator random fields) and examines
the question of whether the variogram of a member of these two families could be spherical, circular, or triangular. It is
shown that there are such examples in one-dimensional spaces, while there are counterexamples in higher-dimensional spaces
for mosaic random fields, indicators of Boolean random sets and indicators of excursion sets of Gaussian random fields. Further
results concerning the spherical plus nugget and circular plus nugget variograms are provided. |
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