Non-linear Shot Noise: Lévy, Noah, & Joseph

The resulting Shot Noise admits an underlying Lévy structure-which we explicitly compute, and can yield both the Noah effect and the Joseph effect. Closed-form analytic formulae for various statistics are derived, including: the log-Laplace transform and cumulants of the stationary noise level; the process' auto-covariance function; and, the process' range-of-dependence.