关于平稳高斯过程的上穿过期望次数的几点注记

Notes on Mean Number of Upcrossings for Stationary Gaussian Process

设｛Ｘ（ｔ），０≤ｔ≤Ｔ＜＋∞｝是平稳高斯过程（可以是均方不可微的，即二阶谱矩可以是无限的），本文着重讨论当ｎ→∞时，过程上穿过ｕ的期望次数的渐近性质．

Let {X (t), 0 < t≤T < + ∞ } be a stationary Gaussian process (may be nondifferentiable in quadratic mean). We discuss the asymptotical properties of mean number of upcrossings for level u > 0 (or u →∞) by {X(t),0≤ t≤ T }.