  We propose a simple method that allows, in one dimension, to solve exactly a
wide class of classical stochastic many-body systems far from equilibrium. For
the sake of illustration and without loss of generality, we focus on a model
that describes the asymmetric diffusion of hard core particles in the presence
of an external source and instantaneous annihilation. Starting from a Master
equation formulation of the problem we show that the density and multi-point
correlation functions obey a closed set of integro-differential equations which
in turn can be solved numerically and/or analytically
