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- W2080237439 abstract "Let ${X_n, n geqq 1}$ be a real-valued, stationary Gaussian sequence with mean zero and variance one. Let $M_n = max_{1leqq ileqq n} X_i, r_n = E(X_{n+1}X_1); c_n = (2 ln n)^{frac{1}{2}}$ and $b_n = c_n - frac{1}{2}lbrackln (4pi ln n)rbrack/c_n$. Define $U_n = 2c_n(M_n - c_n)/lnln n$ and $V_n = c_n(M_n - b_n)$. If $r_n = O(1/ln n)$ as $n rightarrow infty$ then (i) $p(lim inf_{nrightarrowinfty} U_n = -1) = p(lim sup_{nrightarrowinfty} U_n = 1) = 1$, and (ii) $E{exp(tV_n)} rightarrow E{exp (tX)}$ as $n rightarrow infty$ for all $t$ sufficiently small where $X$ is a random variable with distribution function $e^{-e^{-x}}; -infty < x < infty$." @default.
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- W2080237439 date "1974-04-01" @default.
- W2080237439 modified "2023-09-24" @default.
- W2080237439 title "Limiting Behavior of Maxima in Stationary Gaussian Sequences" @default.
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- W2080237439 doi "https://doi.org/10.1214/aop/1176996705" @default.
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