  It is well known that some quantum and statistical fluctuations of a quantum
field may be recovered by adding suitable stochastic sources to the mean field
equations derived from the Schwinger-Keldysh (Closed-time-path) effective
action. In this note we show that this method can be extended to higher
correlations and higher (n-particle irreducible) effective actions. As an
example, we investigate three and fourth order correlations by adding
stochastic sources to the Schwinger - Dyson equations derived from the
2-particle irreducible effective. This method is a simple way to investigate
the nonlinear dynamics of quantum fluctuations.
