In this paper we study the asymptotic behavior of solutions of a
first-order stochastic lattice dynamical system with a multiplicative
noise.
We do not assume any Lipschitz condition on the nonlinear term,
just a continuity assumption together with growth and dissipative
conditions, so that uniqueness of the Cauchy problem fails to be
true.
Using the theory of multi-valued random dynamical systems we
prove the existence of a random compact global attracto