  In this paper we study a system of stochastic differential equations with
dissipative nonlinearity which arise in certain neurobiology models. Besides
proving existence, uniqueness and continuous dependence on the initial datum,
we shall be mainly concerned with the asymptotic behaviour of the solution. We
prove the existence of an invariant ergodic measure $\nu$ associated with the
transition semigroup $P_t$; further, we identify its infinitesimal generator in
the space $L^2(H;\nu)$.
