  We consider the asymmetric random average process which is a one-dimensional
stochastic lattice model with nearest neighbour interaction but continuous and
unbounded state variables. First, the explicit functional representations,
so-called beta densities, of all local interactions leading to steady states of
product measure form are rigorously derived. This also completes an outstanding
proof given in a previous publication. Then, we present an alternative solution
for the processes with factorized stationary states by using a matrix product
ansatz. Due to continuous state variables we obtain a matrix algebra in form of
a functional equation which can be solved exactly.
