Centered stochastic shells of deterministic systems (Q1930811)

A class of stochastic systems called centered stochastic systems is considered. This class is built upon two components, a deterministic system \(D\) and its perturbed version \(S\). The stochastic component \(S\) traces (in the mean sense) the system \(D\) which is described in terms of input and output variables with a componentwise decomposable functional. A universal probability distribution law for the values of the observed output variables is determined by a family of probability measures with the state space of the system \(D\) as its parameter. This law is specified by various functionals, including linear and quadratic forms on Hilbert spaces. This study can also be considered as universalization of some approaches to statistical foundations of quantum mechanics.