The terms of the series are orthogonal (uncorrelated) with respect to a statistical input of white noise.
In this context, the series approximates the functional relation of the output to the entire history of system input at any time.
The Wiener series has been applied mostly to the identification of biological systems, especially in neuroscience.
In the mathematical literature it occurs as the Itô expansion (1951) which has a different form but is entirely equivalent to it.
where the input is white noise with zero mean value and power A, we can write the output of the system as sum of a series of Wiener G-functionals