  The spectrum of the evolution Operator associated with a nonlinear stochastic
flow with additive noise is evaluated by diagonalization in a polynomial basis.
The method works for arbitrary noise strength. In the weak noise limit we
formulate a new perturbative expansion for the spectrum of the stochastic
evolution Operator in terms of expansions around the classical periodic orbits.
The diagonalization of such operators is easier to implement than the standard
Feynman diagram perturbation theory. The result is a stochastic analog of the
Gutzwiller semiclassical spectral determinant with the ``$\hbar$'' corrections
computed to at least two orders more than what has so far been attainable in
stochastic and quantum-mechanical applications, supplemented by the estimate
for the late terms in the asymptotic saddlepoint expansions.
