In this paper we study a
stochastic partial equation of the following form.
where f is a monotone nonlinear operator and α is a “white noise” process in x and
t. In a previous paper we demonstrated the existence of a unique solution in a
generalized sense for x in a bounded domain. This solution was decomposed into the
sum of a stationary process and a transient process. An explicit representation was
found for the stationary distribution of the stationary process. If f is an ordinary
function of u(x) then the stationary distribution is associated with a Markov process
in x. The purpose of this paper is to remove the restriction of boundedness for the
bounded domain.
