Nonlinear statistical signal processing: Useful theorems and their application

A coherent treatment is presented of Price’s theorem, Pawula’s theorem and Bonnet’s theorem. These theorems are often used for the computation of the expectation of nonlinear functions of normally distributed stochastic variables or stochastic processes. In addition, a number of modifications and simplifications of these theorems is proposed. Finally, a class of non-normal distributions for which the theorems are true is briefly discussed.