Spectrum of stochastic evolution operators: Local matrix representation approach

A matrix representation of the evolution operator associated with a nonline ar stochastic flow with additive noise is used to compute its spectrum. In the weak noise limit a perturbative expansion for the spectrum is formulate d in terms of local matrix representations of the evolution operator center ed on classical periodic orbits. The evaluation of perturbative corrections is easier to implement in this framework than in the standard Feynman diag ram perturbation theory. The results are perturbative corrections to a stoc hastic analog of the Gutzwiller semiclassical spectral determinant computed to several orders beyond what has so far been attainable in stochastic and quantum-mechanical applications. [S1063-651X(99)10210-1].