Neural network approximation of stochastic processes: A recursive algorithm

Artificial Neural Networks (ANNs) must be able to learn by experience from environment. Some neural networks are capable of approximating not only deterministic (non-random) functions but also stochastic processes. These networks, named Stochastic Neural Networks represents a generalisation of the usually defined neural networks. From an application point of view such a class of networks is more adherent to the real world whose nature is essentially stochastic. In this paper an original recursive training algorithm for the approximation of a large class of stochastic process has been presented. The methodology is based on the canonical representation of non-stationary stochastic processes by means of Brownian motion processes.