Definition
The stationarity concept refers to the translation invariance of all or some statistical characteristics of a random function (also referred to as random field or spatial stochastic process). A random function is called strictly stationary if its spatial distribution is invariant under spatial shifts. Second-order (or weakly or wide-sense) stationarity for a random function means that its first- and second-order moments are translation invariant. A random function is said to be intrinsically stationary if its increments are second-order (or weakly or wide-sense) stationary random functions. A random function is said to be locally (or quasi) second-order stationary if its first two moments are approximately stationary at any given position of a neighborhood moved around in the study domain.
Introduction
A classical problem in geosciences is predicting a spatially continuous variable of interest over the whole study region, from measurements taken at some locations. Examples...
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Fouedjio, F. (2021). Stationarity. In: Daya Sagar, B., Cheng, Q., McKinley, J., Agterberg, F. (eds) Encyclopedia of Mathematical Geosciences. Encyclopedia of Earth Sciences Series. Springer, Cham. https://doi.org/10.1007/978-3-030-26050-7_428-1
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DOI: https://doi.org/10.1007/978-3-030-26050-7_428-1
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