It has applications related to predicting extreme events, such as major earthquakes and floods.
[3] Consider a scalar, zero-mean Gaussian process y(t) with variance σy2 and power spectral density Φy(f), where f is a frequency.
[1] For power spectral densities that decay less steeply than f−3 as f→∞, the integral in the numerator of N0 does not converge.
Hoblit gives methods for approximating N0 in such cases with applications aimed at continuous gusts.
The interarrival times of this Poisson process are exponentially distributed with rate of decay equal to the frequency of exceedance N(ymax).