Let {X（t）, t ≥ 0} be a standard（zero-mean, unit-variance） stationary Gaussian process with correlation function r（·） and continuous sample paths. In this paper, we consider the maxima M（T） = max{X（t）, ...Let {X（t）, t ≥ 0} be a standard（zero-mean, unit-variance） stationary Gaussian process with correlation function r（·） and continuous sample paths. In this paper, we consider the maxima M（T） = max{X（t）, t∈ [0, T ]} with random index TT, where TT /T converges to a non-degenerate distribution or to a positive random variable in probability, and show that the limit distribution of M（TT） exists under some additional conditions related to the correlation function r（·）.展开更多
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...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 → ∞.展开更多
We propose a method for estimating mean squared error and bandwidth in the windowedspectral density estimation of a stationary Gaussian process, and also provide a method forestimating the second order derivative of t...We propose a method for estimating mean squared error and bandwidth in the windowedspectral density estimation of a stationary Gaussian process, and also provide a method forestimating the second order derivative of the spectral density function. The asymptotic propertiesand the convergence rates of the estimators are given.展开更多
基金Supported by National Science Foundation of China(Grant No.11326175)Research Start-up Foundation of Jiaxing University(Grant No.70512021)
文摘Let {X（t）, t ≥ 0} be a standard（zero-mean, unit-variance） stationary Gaussian process with correlation function r（·） and continuous sample paths. In this paper, we consider the maxima M（T） = max{X（t）, t∈ [0, T ]} with random index TT, where TT /T converges to a non-degenerate distribution or to a positive random variable in probability, and show that the limit distribution of M（TT） exists under some additional conditions related to the correlation function r（·）.
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)+1 种基金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)
文摘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 → ∞.
文摘We propose a method for estimating mean squared error and bandwidth in the windowedspectral density estimation of a stationary Gaussian process, and also provide a method forestimating the second order derivative of the spectral density function. The asymptotic propertiesand the convergence rates of the estimators are given.
