Functional calculus in the theory of nonlinear systems with stochastic signals

Connections between the theorems of Bussgang, Price, McMahon, Novikov, and Wiener are established, and new theorems are introduced for nonlinear functionals of Gaussian random processes by the use of functional calculus. In particular, Novikov's formula is extended to obtain an expression for the Wiener-Hermite kernels of a functional in terms of its functional derivatives.