**C. P. Dettmann**

**May 15, 1998**

Dept. of Physics and Astronomy, Northwestern University, Evanston
IL 60208

cpd@snowmass.phys.nwu.edu

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
with moderate
to strong additive Gaussian noise, rapid convergence is demonstrated for
all values of
with strong noise as well as at fixed
for all noise levels.

PACS: 05.45.+b 02.50.Ey 02.60.Jh