Complexity and irreversibility in stochastic analysis

We discuss complexity of random phenomena which can be expressed as functionals of white noise . This white noise is realized as the time derivative of a Brownian motion B(t), and the collection , is a system of idealized elemental variables. Having expressed the given random phenomena in question in terms of the we introduce the notion of multiplicity in time evolution, which describes how much the phenomena are complex. A white noise is a system which is time oriented, so that one can speak of the time reversibility and irreversibility of certain random phenomena in terms of the white noise. Then, applicability of the theory to quantum dynamics can be considered.