ABSTRACT
B. B. Mandelbrot and J. R. Wallis observed that models with infinite variance are more appropriate for many hydrological series. In analogy to the "Joseph effect," they call the phenomenon of an infinite variance the "Noah effect." Generally speaking, infinite variance processes are good model candidates for "bursty" phenomena, i.e., phenomena that exhibit occasional unusually large observations. There is an extensive literature on the probability theory for infinite variance processes. Many methods exist for simulating Gaussian processes. The most obvious method is to multiply a vector of iid standard normal random variables by a suitable transformation matrix. As Brownian motion has independent increments, the only random numbers one needs to generate are iid standard normal variables. More details and several versions of this approximation are given in Mandelbrot and Mandelbrot and Wallis. One simulates a sufficient number of short-memory processes with parameters chosen randomly from a certain distribution.
