  The aim of the article is to develop the stochastic interpretation of quantum
mechanics by E. Nelson on the basis of balancing the intra-systemic
contradiction (i.e., antisymmetry) between "order" and "chaos". For the set
task, it is proposed to combine two mutually opposite system-forming
principles: "the principle of least action" and "the principle of maximum
entropy" into one the "principle of averaged efficiency extremum". In a
detailed consideration of the averaged states of a chaotically wandering
particle, the time-independent (stationary) and time-dependent stochastic
Schrodinger-Euler-Poisson equations are obtained as conditions for finding the
extremals of the functional of the globally averaged efficiency functional of
the stochastic system under study. The resulting stochastic equations coincides
with the corresponding Schrodinger equations up to coefficients. In this case,
the ratio of the reduced Planck constant to the particle mass is expressed
through the averaged characteristics of a three-dimensional random process in
which the considered wandering particle participates. The obtained stochastic
equations are suitable for describing the quantum states of stochastic systems
of any scale.
