  We consider an evolution operator for a discrete Langevin equation with a
strongly hyperbolic classical dynamics and noise with finite moments. Using a
perturbative expansion of the evolution operator we calculate high order
corrections to its trace in the case of a quartic map and Gaussian noise. The
leading contributions come from the period one orbits of the map. The
asymptotic behaviour is investigated and is found to be independent up to a
multiplicative constant of the distribution of noise.
