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April, 1972 Upper Bounds for the Asymptotic Maxima of Continuous Gaussian Processes
M. B. Marcus
Ann. Math. Statist. 43(2): 522-533 (April, 1972). DOI: 10.1214/aoms/1177692633


Upper bounds are obtained for $|X(t)|/Q(t)$ as $t \rightarrow \infty$, where $X(t)$ is a continuous Gaussian process with $EX^2(t) \leqq Q^2(t), Q(t)$ non-decreasing. Our results are extensions of some work of Pickands (1967), Nisio (1967) and Orey (1971) to larger classes of Gaussian processes, i.e. fewer restrictions are imposed on the covariance functions. The results follow from Fernique's lemma (1964) and a recent lemma on the maximum of Gaussian sequences due to Landau, Shepp, Fernique and the author (see Marcus, Shepp (1971) for further references to this lemma).


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M. B. Marcus. "Upper Bounds for the Asymptotic Maxima of Continuous Gaussian Processes." Ann. Math. Statist. 43 (2) 522 - 533, April, 1972.


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

zbMATH: 0241.60032
MathSciNet: MR388519
Digital Object Identifier: 10.1214/aoms/1177692633

Rights: Copyright © 1972 Institute of Mathematical Statistics


Vol.43 • No. 2 • April, 1972
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