Study of stochastic differential equations by constructive methods. I

In this work we give an algorithm to express as a convergent series the stationary averages for a class of gradient perturbations of a nonsymmetric (nongradient) Ornstein-Uhlenbeck process. The method relies on a cluster expansion in time of the Girsanov-Cameron-Martin formula for the density of the perturbed measure with respect to the Ornstein-Uhlenbeck measure. In the second paper of this series, the approach is extended to more general perturbations