Asymptotic analysis of P.D.E.s with wide–band noise disturbances, and expansion of the moments

We present an asymptotic analysis -in the “ white-noise limit”- of a linear parabolic partial differential equation, whose coefficients are perturbed by a wide-band noise. After having studied some ergodic properties of a class of diffusion processes, we prove the convergence in law towards the solution of an Ito stochastic P.D.E. We then establish an expansion in powers of Δ ( 1/Δ being a measure of the bandwith of the driving noise) of the first moment of the solution