  Using a method of stochastic perturbation of a Langevin system associated
with the non-viscous Burgers equation we construct a solution to the Riemann
problem for the pressureless gas dynamics describing sticky particles. As a
bridging step we consider a medium consisting of noninteracting particles. We
analyze the difference in the behavior of discontinuous solutions for these two
models and the relations between them. In our framework we obtain a unique
entropy solution to the Riemann problem in 1D case. Moreover, we describe how
starting from smooth data a $\delta$ - singularity arises in one component of
the solution.
