Some properties of a normal process near a local maximum
Consider a stationary normal process ξ(t) with mean zero and the covariance function r(t). Properties of the sample functions in the neighborhood of zeros, upcrossings of very high levels, etc. have been studied by, among others, Kac and Slepian, 1959 [4] and Slepian, 1962 [11]. In this paper we shall study the sample functions near local maxima of height u, especially as u → -∞, and mainly use si