Traces and determinants of strongly stochastic operators

Periodic orbit theory allows calculations of long-time properties of chaoti c systems from traces, dynamical zeta functions, and spectral determinants of deterministic evolution operators, which are in turn evaluated in terms of periodic orbits. For the case of stochastic dynamics a direct numerical evaluation of the trace of an evolution operator is possible as a multidime nsional integral. Techniques for evaluating such path integrals are discuss ed. Using as an example the logistic map f(x) = lambda x(1 - x) with modera te to strong additive Gaussian noise, rapid convergence is demonstrated for all values of lambda with strong noise as well as at fixed lambda = 5 for all noise levels. [S1063-651X(99)10604-4].