Asymptotic properties of Gaussian random fields
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- by Clifford Qualls and Hisao Watanabe PDF
- Trans. Amer. Math. Soc. 177 (1973), 155-171 Request permission
Abstract:
In this paper we study continuous mean zero Gaussian random fields $X(p)$ with an N-dimensional parameter and having a correlation function $\rho (p,q)$ for which $1 - \rho (p,q)$ is asymptotic to a regularly varying (at zero) function of the distance ${\text {dis}}\;(p,q)$ with exponent $0 < \alpha \leq 2$. For such random fields, we obtain the asymptotic tail distribution of the maximum of $X(p)$ and an asymptotic almost sure property for $X(p)$ as $|p| \to \infty$. Both results generalize ones previously given by the authors for $N = 1$.References
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Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 177 (1973), 155-171
- MSC: Primary 60G15
- DOI: https://doi.org/10.1090/S0002-9947-1973-0322943-8
- MathSciNet review: 0322943