Global solution of the pressureless gas equation with viscosity

We construct a global weak solution to a d-dimensional system of zero-pressure gas dynamics modified by introducing a finite artificial viscosity. We use discrete approximations to the continuous gas and make particles move along trajectories of the normalized simple symmetric random walk with deterministic drift. The interaction of these particles is given by a sticky particle dynamics. We show that a subsequence of these approximations converges to a weak solution of the system of zero-pressure gas dynamics in the sense of distributions. This weak solution is interpreted in terms of a random process solution of a nonlinear stochastic differential equation. We get a weak solution of the inviscid system by tending the viscosity to zero.