Nonclassical Brownian motions , stochastic flows , continuous products . I

Contrary to the classical wisdom, processes with independent values (defined properly) are much more diverse than white noise combined with Poisson point processes, as well as product systems are much more diverse than Fock spaces. This text is the first part of a survey of recent progress in constructing and investigating nonclassical Brownian motions, stochastic flows and continuous products of probability spaces and Hilbert spaces.