A note on the functional law of iterated logarithm for maxima of Gaussian sequences |
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Authors: | Jürg Hüsler |
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Institution: | University of Bern, Bern, Switzerland |
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Abstract: | Let {Xn, n ≥ 1} be a real-valued stationary Gaussian sequence with mean zero and variance one. Let Mn = max{Xt, i ≤ n} and Hn(t) = (Mnt] ? bn)an?1 be the maximum resp. the properly normalised maximum process, where , and . We characterize the almost sure limit functions of (Hn)n≥3 in the set of non-negative, non-decreasing, right-continuous, real-valued functions on (0, ∞), if r(n) (log n)3?Δ = O(1) for all Δ > 0 or if r(n) (log n)2?Δ = O(1) for all Δ > 0 and r(n) convex and fulfills another regularity condition, where r(n) is the correlation function of the Gaussian sequence. |
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Keywords: | 60G15 Law of iterated logarithm maximum Gaussian sequences |
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