  We address the problem of constructing a non-equilibrium stationary state for
a one-dimensional stochastic Klein-Gordon wave equation with non-linearity,
using perturbation theory. The linear theory is reviewed, but with the linear
equations of motion including an additional potential term which emerges in the
renormalization of the perturbation expansion for the state corresponding to
the non-linear equations of motion. The potential is the solution to a fixed
point equation. Low order terms in the expansion for the two-point function are
determined.
