Contrary to the classical wisdom, processes with independent values (defined properly) are much more diverse than white noises combined with Poisson point processes, and product systems are much more diverse than Fock spaces.
This text is a survey of recent progress in constructing and investigating nonclassical stochastic flows and continuous products of probability spaces and Hilbert spaces.
"Nonclassical stochastic flows and continuous products." Probab. Surveys 1 173 - 298, 2004. https://doi.org/10.1214/154957804100000042