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

Reinhard Furrer and Michael Hediger

Stochastic Processes and their Applications, 2024, vol. 173, issue C

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.

Keywords: Gaussian random fields; Stationarity; Isotropy; Equivalence of Gaussian measures; Orthogonality of Gaussian measures (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spa.2024.104356

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