  Nonlinear conservation laws subject to random initial conditions pose
fundamental problems in the evolution and interactions of shocks and
rarefactions. Using a discrete set of values for the solution, we derive a
hierarchy of equations in terms of the states in two different methods. This
hierarchy involves the n-point function, the probability that the solution
takes on various values at different positions, in terms of the n+1-point
function. In the first approach, these equations can be closed but the
resulting solutions do not persist through shock interactions. In our second
approach, the n-point function is expressed in terms of the n+1-point
functions, and remains valid through collisions of shocks.
