  The formalism of the particle dynamics in the space-time, where motion of
free particles is primordially stochastic, is considered. The conventional
dynamic formalism, obtained for the space-time, where the motion of free
particles is primordially deterministic, seems to be unsuitable. The
statistical ensemble of stochastic (or deterministic) systems is considered to
be the main object of dynamics. At such a logical reloading the statistical
description becomes a component of dynamics, and capacities of dynamics
increase. At such an approach one can describe deterministic, stochastic and
quantum particles by means of the uniform technique. The quantum particle is
described as a stochastic particle, i.e. without a reference to the quantum
principles. Besides, by means of this technique one can describe classical
inviscid fluid. There are four different versions of the formalism: (1)
description in Euler dynamic variables, (2) description in Lagrange dynamic
variables, (3) description in terms of the generalized stream function, (4)
description in terms of the wave function. The uniform formalism is purely
dynamic. Even describing stochastic systems, it does not refer to probability
and probabilistic structures. In relativistic case the uniform formalism can
describe pair production and pair annihilation.
