{x(t),0≤t≤T)为均方可微非平稳高斯过程,具有渐近中心化的均值m(t)和常数的方差,NT(·)为{x(t),0≤t≤T)上穿过水平UT的点过程,则在一定的条件下上穿过点过程NT(·)依分布收敛到一Poisson过程.
Abstract Let {X(t), 0 ≤ t ≤ T} be a non-stationary and differentiable Gaussian process with asymptotic centered mean re(t) and constant variance. Let NT(·) be the number of upcrossings of level UT by the process X(t) on the interval [0, T]. Under some conditions, the point process NT(·) formed by the number of upcrossings converges in distribution to a Poisson process.