Reducing non-stationary random fields to stationarity and isotropy using a space deformation

By Olivier Perrin, R. Senoussi. 2000

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Nonstationary spatial covariance functions (2005, background): “Another approach to producing explicit covariance functions with locally varying geometric anisotropies is to use spatial deformations (Sampson and Guttorp 1992, Perrin and Senoussi 2000, Sampson, Damian and Guttorp 2001, Schmidt and O’Hagan 2003, Clerc and Mallat 2003).”
Second-order non-stationary modeling approaches for univariate geostatistical data (2017, methodology): “…inverse and the function c0ð Þ, then the space deformation model is identifiable up to a scaling for c0ð Þ and up to a homothetic Euclidean motion for f ð Þ. Perrin and Senoussi (2000) give a characterization of non-stationary correlation functions reducible to stationary or isotropic…”
Classes of Kernels for Machine Learning: A Statistics Perspective (2002, background): “Perrin and Senoussi ( 1999 , 2000 ) characterize such deformations Φ .”
Nonstationary covariance models for global data (2008, methodology): “Spatial deformations to model nonstationary spatial processes have been used, for example, in Sampson and Guttorp (1992), Perrin and Senoussi (2000), Schmidt and O’Hagan (2003), Clerc and Mallat (2003) and Anderes and Stein (2008).”