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Properties of Random Fields

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Abstract

This chapter provides the necessary background on random fields for understanding the subsequent chapters on prediction and inference for random fields. The focus here is on weakly stationary random fields (defined later in this section) and the associated spectral theory. Some previous exposure to Fourier methods is assumed. A knowledge of the theory of characteristic functions at the level of a graduate course in probability (see, for example, Billingsley (1995), Chung (1974), or Feller (1971)) should, for the most part, suffice. When interpolating a random field, the local behavior of the random field turn out to be critical (see Chapter 3). Accordingly, this chapter goes into considerable detail about the local behavior of random fields and its relationship to spectral theory.

Keywords

  • Spectral Density
  • Random Field
  • Covariance Function
  • Tauberian Theorem
  • Gaussian Random Field

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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  • DOI: 10.1007/978-1-4612-1494-6_2
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© 1999 Springer Science+Business Media New York

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Stein, M.L. (1999). Properties of Random Fields. In: Interpolation of Spatial Data. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1494-6_2

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  • DOI: https://doi.org/10.1007/978-1-4612-1494-6_2

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7166-6

  • Online ISBN: 978-1-4612-1494-6

  • eBook Packages: Springer Book Archive