In probability theory, an excursion probability is the probability that a stochastic process surpasses a given value in a fixed time period.
It is the probability[1] Numerous approximation methods for the situation where u is large and f(t) is a Gaussian process have been proposed such as Rice's formula.
[1][2] First-excursion probabilities can be used to describe deflection to a critical point experienced by structures during "random loadings, such as earthquakes, strong gusts, hurricanes, etc.
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