A note on the functional law of iterated logarithm for maxima of Gaussian sequences

Jürg Hüsler

Journal of Multivariate Analysis, 1981, vol. 11, issue 2, 273-279

Abstract: Let {Xn, n >= 1} be a real-valued stationary Gaussian sequence with mean zero and variance one. Let Mn = max{Xt, i =3 in the set of non-negative, non-decreasing, right-continuous, real-valued functions on (0, [infinity]), if r(n) (log n)3-[Delta] = O(1) for all [Delta] > 0 or if r(n) (log n)2-[Delta] = O(1) for all [Delta] > 0 and r(n) convex and fulfills another regularity condition, where r(n) is the correlation function of the Gaussian sequence.

Keywords: Law; of; iterated; logarithm; maximum; Gaussian; sequences (search for similar items in EconPapers)
Date: 1981
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