LECTURES ON WHITE NOISE FUNCTIONALS

White noise analysis is an advanced stochastic calculus that has developed extensively since three decades ago. It has two main characteristics. One is the notion of generalized white noise functionals, the introduction of which is oriented by the line of advanced analysis, and they have made much contribution to the fields in science enormously. The other characteristic is that the white noise analysis has an aspect of infinite dimensional harmonic analysis arising from the infinite dimensional rotation group. With the help of this rotation group, the white noise analysis has explored new areas of mathematics and has extended the fields of applications.
Contents: Generalized White Noise Functionals; Elemental Random Variables and Gaussian Processes; Linear Processes and Linear Fields; Harmonic Analysis Arising from Infinite Dimensional Rotation Group; Complex White Noise and Infinite Dimensional Unitary Group; Characterization of Poisson Noise; Innovation Theory; Variational Calculus for Random Fields and Operator Fields; Four Notable Roads to Quantum Dynamics.