Higher Order Hydrodynamic Equations for a System of Independent Random Walks

Abstract

We describe a construction that permits us to define hydrodynamic equations of higher order for a system of independent particles which perform homogeneous random walks. The main result states that, under some conditions on the increments of the random walk, the solution of the hydrodynamic equations of order n approximates the density of the original particle dynamics uniformly on time intervals [0, ∈−(n− γ)] for any γ > 0. Here ∈ is the small parameter used in the definition of the hydrodynamic limit.