On the approximation of stochastic processes by approximate identity neural networks

The ability of a neural network to learn from experience can be viewed as closely related to its approximating properties. By assuming that environment is essentially stochastic it follows that neural networks should be able to approximate stochastic processes. The aim of this paper is to show that some classes of artificial neural networks exist such that they are capable of providing the approximation, in the mean square sense, of prescribed stochastic processes with arbitrary accuracy. The networks so defined constitute a new model for neural processing and extend previous results concerning approximating capabilities of artificial neural networks.