  We study the transition from the full quantum mechanical description of
physical systems to an approximate classical stochastic one. Our main tool is
the identification of the closed-time-path (CTP) generating functional of
Schwinger and Keldysh with the decoherence functional of the consistent
histories approach. Given a degree of coarse-graining in which interferences
are negligible, we can explicitly write a generating functional for the
effective stochastic process in terms of the CTP generating functional. This
construction gives particularly simple results for Gaussian processes. The
formalism is applied to simple quantum systems, quantum Brownian motion,
quantum fields in curved spacetime. Perturbation theory is also explained. We
conclude with a discussion on the problem of backreaction of quantum fields in
spacetime geometry.
