Abstract
Let ξ(t) be a zero-mean stationary Gaussian process with the covariance function r(t) of Pickands type, i.e., r(t) = 1 − |t|α + o(|t|α), t → 0, 0 < α ≤ 2, and η(t), ζ(t) be periodic random processes. The exact asymptotic behavior of the probabilities P(max t∈[0,T] η(t)ξ(t) > u), P(max t∈[0,T] (ξ(t) + η(t)) > u) and P(max t∈[0,T] (η(t)ξ(t) + ζ(t)) > u) is obtained for u → ∞ for any T > 0 and independent ξ(t), η(t), ζ(t).
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Original Russian Text © A.O. Kleban and M.V. Korulin, 2017, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2017, Vol. 72, No. 1, pp. 11–16.
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Kleban, A.O., Korulin, M.V. Probabilities of high extremes for a Gaussian stationary process in a random environment. Moscow Univ. Math. Bull. 72, 10–14 (2017). https://doi.org/10.3103/S0027132217010028
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DOI: https://doi.org/10.3103/S0027132217010028