  Binary particle coagulation can be modelled as the repeated random process of
the combination of two particles to form a third. The kinetics can be
represented by population rate equations based on a mean field assumption,
according to which the rate of aggregation is taken to be proportional to the
product of the mean populations of the two participants. This can be a poor
approximation when the mean populations are small. However, using the Poisson
representation it is possible to derive a set of rate equations that go beyond
mean field theory, describing pseudo-populations that are continuous, noisy and
complex, but where averaging over the noise and initial conditions gives the
mean of the physical population. Such an approach is explored for the simple
case of a size-independent rate of coagulation between particles. Analytical
results are compared with numerical computations and with results derived by
other means. In the numerical work we encounter instabilities that can be
eliminated using a suitable 'gauge' transformation of the problem [P. D.
Drummond, Eur. Phys. J. B38, 617 (2004)] which we show to be equivalent to the
application of the Cameron-Martin-Girsanov formula describing a shift in a
probability measure. The cost of such a procedure is to introduce additional
statistical noise into the numerical results, but we identify an optimised
gauge transformation where this difficulty is minimal for the main properties
of interest. For more complicated systems, such an approach is likely to be
computationally cheaper than Monte Carlo simulation.
