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On the orthogonality of zero-mean Gaussian measures: Sufficiently dense sampling

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  • Furrer, Reinhard
  • Hediger, Michael

Abstract

For a stationary random function ξ, sampled on a subset D of Rd, we examine the equivalence and orthogonality of two zero-mean Gaussian measures P1 and P2 associated with ξ. We give the isotropic analog to the result that the equivalence of P1 and P2 is linked with the existence of a square-integrable extension of the difference between the covariance functions of P1 and P2 from D to Rd. We show that the orthogonality of P1 and P2 can be recovered when the set of distances from points of D to the origin is dense in the set of non-negative real numbers.

Suggested Citation

  • Furrer, Reinhard & Hediger, Michael, 2024. "On the orthogonality of zero-mean Gaussian measures: Sufficiently dense sampling," Stochastic Processes and their Applications, Elsevier, vol. 173(C).
    • Handle: RePEc:eee:spapps:v:173:y:2024:i:c:s0304414924000620
    DOI: 10.1016/j.spa.2024.104356
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    References listed on IDEAS

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    1. Zhang, Hao, 2004. "Inconsistent Estimation and Asymptotically Equal Interpolations in Model-Based Geostatistics," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 250-261, January.
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