Journal of Statistical Physics, Vol. 101, Nos. 12, 2000, p. 385-395.
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 asymptotic behaviour is investigated and is found to be independent up to a multiplicative constant of the distribution of noise.