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Let {Xn, n ≥ 0} be a stationary Gaussian sequence of standard normal random variables with covariance function r(n) = EX0Xn. Let 
Under some mild regularity conditions on r(n) and the condition that r(n)lnn = o(1) or (r(n)lnn)−1 = O(1), the asymptotic distribution of 
is obtained. Continuous-time results are also presented as well as a tube formula tail area approximation to the joint distribution of the sum and maximum.
