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April, 1972 Asymptotic Properties of Gaussian Processes
Clifford Qualls, Hisao Watanabe
Ann. Math. Statist. 43(2): 580-596 (April, 1972). DOI: 10.1214/aoms/1177692638


We study separable mean zero Gaussian processes $X(t)$ with correlation $\rho (t, s)$ for which $1 - \rho (t, s)$ is asymptotic to a regularly varying (at zero) function of $|t - s|$ with exponent $0 < \alpha \leqq 2$. For such processes, we obtain the asymptotic distribution of the maximum of $X(t)$. This result is used to obtain a result for $X(t)$ as $t \rightarrow \infty$ similar to the so-called law of the iterated logarithm.


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Clifford Qualls. Hisao Watanabe. "Asymptotic Properties of Gaussian Processes." Ann. Math. Statist. 43 (2) 580 - 596, April, 1972.


Published: April, 1972
First available in Project Euclid: 27 April 2007

zbMATH: 0247.60031
MathSciNet: MR307318
Digital Object Identifier: 10.1214/aoms/1177692638

Rights: Copyright © 1972 Institute of Mathematical Statistics

Vol.43 • No. 2 • April, 1972
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