Abstract

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