Particle motion in stochastic space, i.e., space whose coordinates consist of small, regular stochastic parts, is considered. A free particle in this space resembles a Brownian particle the motion of which is characterized by a dispersionD dependent on the universal length l. It is shown that in the first approximation in the parameter l the particle motion in an external force field is described by equations coincident in form with equations of stochastic mechanics due to Nelson, Kershow, and de la (...) Pena-Auerbach. A method is proposed for the relativization of the scheme used to describe the processes in the stochastic space; by using this method, the equations of particle motion can be written in a covariant form. (shrink)

Within the framework of the Kershaw approach and of a hypothesis on spatial stochasticity, the relativistic equations of Lehr and Park, Guerra and Ruggiero, and Vigier for stochastic Nelson mechanics are obtained. In our model there is another set of equations of the hydrodynamical type for the drift velocityv i(x j,t) and stochastic velocityu i(x j,t) of a particle. Taking into account quadratic terms in l, the universal length, we obtain from these equations the Sivashinsky equations forv i(x j,t) in (...) the caseu i →0. In the limit l →0, these equations acquire the Newtonian form. (shrink)