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Identifiability for non-stationary spatial structure

Part of: Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Olivier Perrin  and
Wendy Meiring
Olivier Perrin*
Affiliation:
INRA
Wendy Meiring*
Affiliation:
University of California, Santa Barbara
*
∗Postal address: GREMAQ-UMR CNRS 5604, Université des Sciences Sociales, Manufacture des Tabacs, Bâtiment F-2ème Étage, 21 Allée de Brienne, 31000 Toulouse, France. Email address: perrin@cict.fr
∗∗Postal address: Statistics and Applied Probability, University of California, Santa Barbara, CA 93106–3110, USA.
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Abstract

For modelling non-stationary spatial random fields Z = {Z(x) : x∊ℝn, n≥2} a recent method has been proposed to deform bijectively the index space so that the spatial dispersion D(x,y) = var[Z(x)-Z(y)], (x,y)∊ℝnxℝn, depends only on the Euclidean distance in the deformed space through an isotropic variogram γ. We prove uniqueness of this model in two different cases: (i) γ is strictly increasing; (ii) γ(u) is differentiable for u > 0.

Keywords

Bijective space deformationdispersion functionisotropyuniquenessvariogram

MSC classification

Primary: 60G60: Random fields
Secondary: 60G12: General second-order processes
Type
Short Communications
Information
Journal of Applied Probability , Volume 36 , Issue 4 , December 1999 , pp. 1244 - 1250
Copyright
Copyright © Applied Probability Trust 1999 

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