Analysis of the stochastic FitzHugh-Nagumo system

In this paper we study a system of stochastic differential equations with dissipative non-linearity which arise incertain neurobiology models. Besides proving existence,unique ness and continuous dependence on the initial datum, we shall mainly be 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).