Stationary Fields

Part of the Springer Monographs in Mathematics book series (SMM)


Stationarity has always been the backbone of almost all examples in the theory of Gaussian processes for which specific computations were possible. As described in the preface, one of the main reasons we shall be studying Gaussian processes on manifolds is to get around this assumption. Nevertheless, despite the fact that we shall ultimately try to avoid it, we invest a chapter on the topic for two reasons:
  • Many of the results of Part III are significantly easier to interpret when specialized down to cases under which stationarity holds.

  • Even in the nonstationary case, many of the detailed computations of Part III can be considered as deriving from a “local conversion to pseudostationarity, ” or, even more so, to pseudoisotropy. This will be taken care of there via the “induced Riemannian metric”defined in Section 12.2. Knowledge of what happens under stationarity is therefore important for knowing what to do in the general case.


Covariance Function Gaussian Process Spherical Harmonic Spectral Measure Spectral Representation 
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© Springer Science+Business Media LLC 2007

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