Invariant measures for stochastic differential equations on networks

Abstract. We study existence and uniqueness of an invariant measure for infinite dimensional stochastic differential equations with dissipative polynomially bounded nonlinear terms. We also exhibit the existence of a density with respect to a Gaussian measure. Moreover, we decompose the solution process into a stationary component and a component which vanishes asymptotically in the L 2 -sense. Applications are given to neurobiological networks where the signals propagation is modelled by a system of coupled stochastic FitzHugh-Nagumo equations.