A note on representation theorems for linear discrete-space systems with stochastic inputs

The cornerstone of the theory of discrete-space single-input-single-output linear systems is the idea that every such system has an input-output map t hat can be represented by a convolution or the familiar generalization of a convolution. This thinking involves an oversight which, for the case of bo unded inputs mapped continuously into bounded outputs, was recently correct ed by adding an additional term to the representation. Here, we give a corr esponding corrected result for discrete-space systems with stochastic input s. Copyright (C) 2001 John Wiley & Sons, Ltd.