  We study the non-equilibrium dynamics of a system of coupled scalar fields in
a Friedmann-Robertson-Walker (FRW) universe. We consider the evolution of
spatially homogeneous "classical" fields and of their quantum fluctuations
including the quantum backreaction in the one-loop approximation. We discuss in
particular the dimensional regularisation of the coupled system and a special
subtraction procedure in order to obtain the renormalised equations of motion
and the renormalised energy-momentum tensor and ensure that the energy is
well-defined and covariantly conserved. These results represent at the same
time a theoretical analysis and a viable scheme for stable numerical
simulations. As an example for an application of the general formalism, we
present simulations for a hybrid inflationary model.
