It has been more than thirty years since white noise analysis was launched systematically. It is now a good time to have an overview of the theory and to reflect on its advantages in order to anticipate further developments of this theory.

Our main interests are in the studies of random complex systems that are developing as time goes by. We first come to the reduction of the complex systems in question.

White noise, that is the time derivative of a Brownian motion, is the most important, elemental system of random variables that can come from the step of the reduction.

We therefore wish to discuss the analysis of functionals of white noise.

Our main interests are in the studies of random complex systems that are developing as time goes by. We first come to the reduction of the complex systems in question.

White noise, that is the time derivative of a Brownian motion, is the most important, elemental system of random variables that can come from the step of the reduction.

We therefore wish to discuss the analysis of functionals of white noise.