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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Supported by the Scientific Research Fund of Sichuan Provincial Education Department (12ZB082), the Scientific research cultivation project of Sichuan University of Science & Engineering (2013PY07), the Scientific Research Fund of Shanghai University of Finance and Economics (2017110080), and the Opening Project of Sichuan Province University Key Laboratory of Bridge Non-destruction Detecting and Engineering Computing (2018QZJ01).
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Lin, Fm., Peng, Zx. Limit theorems for supremum of Gaussian processes over a random interval. Appl. Math. J. Chin. Univ. 33, 335–343 (2018). https://doi.org/10.1007/s11766-018-3438-7
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DOI: https://doi.org/10.1007/s11766-018-3438-7