Summary
Let {X n , n=1, 2, ⋯} be the successive terms of a discrete coordinate stationary Gaussian stochastic process. Assume, without loss of generality, that EX n =0 and r o =EX 2 n =1 for all n. Let r n ≡EX k X k+n be the covariance function. If either there exists an α>0 such that
then
where
It is not sufficient that
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Research sponsored by the National Science Foundation, GP 8716.
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Pickands, J. An iterated logarithm law for the maximum in a stationary gaussian sequence. Z. Wahrscheinlichkeitstheorie verw Gebiete 12, 344–353 (1969). https://doi.org/10.1007/BF00538755
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DOI: https://doi.org/10.1007/BF00538755