摘要
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(sup_(t∈[0,T])X(t) > x) is considered, as x → ∞.
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(sup_(t∈[0,T])X(t) > x) is considered, as x → ∞.
基金
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)
the Opening Project of Sichuan Province University Key Laboratory of Bridge Non-destruction Detecting and Engineering Computing(2018QZJ01)
