  We derive a stochastic path integral representation of counting statistics in
semi-classical systems. The formalism is introduced on the simple case of a
single chaotic cavity with two quantum point contacts, and then further
generalized to find the propagator for charge distributions with an arbitrary
number of counting fields and generalized charges. The counting statistics is
given by the saddle point approximation to the path integral, and fluctuations
around the saddle point are suppressed in the semi-classical approximation. We
use this approach to derive the current cumulants of a chaotic cavity in the
hot-electron regime.
