Some Properties of Large Excursions of a Stationary Gaussian Process
Van Minh Nguyen
Abstract:The present work investigates two properties of level crossings of a stationary Gaussian process X(t) with autocorrelation function R X (τ ). We show firstly that if R X (τ ) admits finite second and fourth derivatives at the origin, the length of up-excursions above a large negative level −γ is asymptotically exponential as −γ → −∞. Secondly, assuming that R X (τ ) admits a finite second derivative at the origin and some defined properties, we derive the mean number of crossings as well as the length of succe… Show more
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