  We formulate the time-dependent Bogoliubov dynamics of colliding
Bose-Einstein condensates in terms of a positive-P representation of the
Bogoliubov field. We obtain stochastic evolution equations for the field which
converge to the full Bogoliubov description as the number of realisations
grows. The numerical effort grows linearly with the size of the computational
lattice. We benchmark the efficiency and accuracy of our description against
Wigner distribution and exact positive-P methods. We consider its regime of
applicability, and show that it is the most efficient method in the common
situation - when the total particle number in the system is insufficient for a
truncated Wigner treatment.
