  We describe a pairing mean-field theory related to the
Hartree-Fock-Bogoliubov approach, and apply it to the dynamics of dissociation
of a molecular Bose-Einstein condensate (BEC) into correlated bosonic atom
pairs. We also perform the same simulation using two stochastic phase-space
techniques for quantum dynamics -- the positive P-representation method and the
truncated Wigner method. By comparing the results of our calculations we are
able to assess the relative strength of these theoretical techniques in
describing molecular dissociation in one spatial dimension. An important aspect
of our analysis is the inclusion of atom-atom interactions which can be
problematic for the positive-P method. We find that the truncated Wigner method
mostly agrees with the positive-P simulations, but can be simulated for
significantly longer times. The pairing mean-field theory results diverge from
the quantum dynamical methods after relatively short times.
