Limit theorems for supremum of Gaussian processes over a random interval |
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| Authors: | Fu-ming Lin Zuo-xiang Peng |
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| Affiliation: | 1.School of Statistics and Management,Shanghai University of Finance and Economics,Shanghai,China;2.School of Mathematics and Statistics,Sichuan University of Science & Engineering,Zigong,China;3.School of Mathematics and Statistics,Southwestern University,Chongqing,China |
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| Abstract: | Let {X(t), t ≥ 0} be a centered stationary Gaussian process with correlation r(t) such that 1 ? r(t) is asymptotic to a regularly varying function. With T being a nonnegative random variable and independent of X(t), the exact asymptotics of P(supt∈[0,T] X(t) > x) is considered, as x → ∞. |
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