  We analyze a systematic algorithm for the exact computation of the current
cumulants in stochastic nonequilibrium systems, recently discussed in the
framework of full counting statistics for mesoscopic systems. This method is
based on identifying the current cumulants from a Rayleigh-Schrodinger
perturbation expansion for the generating function. Here it is derived from a
simple path-distribution identity and extended to the joint statistics of
multiple currents. For a possible thermodynamical interpretation, we compare
this approach to a generalized Onsager-Machlup formalism. We present
calculations for a boundary driven Kawasaki dynamics on a one-dimensional
chain, both for attractive and repulsive particle interactions.
