  Periodic orbit theory allows calculations of long time properties of chaotic
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
multidimensional integral. Techniques for evaluating such path integrals are
discussed. Using as an example the logistic map f(x) = lambda x(1-x) with
moderate 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.
