Quantization Phenomenon in Dynamical Stochastic Systems

The stochastic dynamical system with the states described by elements u of a Hilbert space is considered. There is a deterministic system considered as its nonperturbed variant. An outcome y is observed under random perturbations. The probability distribution P(y, u) of the measurements results in the fixed states u is analysed. A class of stochastic systems marked by the full determination of the law P(y, u) via equations of the nonperturbed system is found. We also find the distributions P(y, u). These distributions prove to be similar to the quantum laws of probability distribution of observable quantities including the principles of superposition and uncertainty and the phenomenon of quantization.