We consider an evolution operator for a discrete Langevin equation with a s
trongly hyperbolic classical dynamics and Gaussian noise. Using an integral
representation of the evolution operator L, we investigate the high-order
corrections to the trace of L-n. The asymptotic behavior is found to be con
trolled by subdominant saddle points previously neglected in the perturbati
ve expansion. We show that a trace formula can be derived to describe the h
igh-order noise corrections.