Quantum-state dynamics as linear representation of classical (nonlinear) stochastic dynamics

We show that the basic equation of the theory of open systems, the Gorini-Kossakowski-Sudarshan-Lindblad equation, as well as its linear and nonlinear generalizations have a natural classical probabilistic interpretation - within the framework of prequantum classical statistical field theory. The latter gives an example of the classical probabilistic model (with random fields as subquantum variables) reproducing the basic probabilistic predictions of quantum mechanics.