Excursion probability explained
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]
P\left\{\suptf(t)\gequ\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.
[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."
[3] Notes and References
- Book: Robert J. . Adler . Jonathan E. . Taylor. 10.1007/978-0-387-48116-6_4 . Excursion Probabilities . Random Fields and Geometry . limited . Springer Monographs in Mathematics . 75–76 . 2007 . 978-0-387-48112-8 .
- Adler . R. J. . 10.1214/aoap/1019737664 . On excursion sets, tube formulas and maxima of random fields . The Annals of Applied Probability. 10 . 1 . 2000 . 2667187. free .
- Yang . J. -N. . First-excursion probability in non-stationary random vibration . 10.1016/0022-460X(73)90059-X . Journal of Sound and Vibration. 27 . 2 . 165–182 . 1973 .
