Excursion probability

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]

\mathbb {P} \left\{\sup _{t\in T}f(t)\geq u\right\}.

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]

References

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