  In this paper, two new stochastic algorithms for calculating parametric
derivatives of the solution to the Smoluchowski coagulation equation are
presented. It is assumed that the coagulation kernel is dependent on these
parameters. The new algorithms (called `Single' and `Double') work by coupling
two Marcus-Lushnikov processes in such a way as to reduce the difference
between their trajectories, thereby significantly reducing the variance of
central difference estimators of the parametric derivatives. In the numerical
results, the algorithms are shown have have a O(1/N) order of convergence as
expected, where N is the initial number of particles. It was also found that
the Single and Double algorithms provide much smaller variances. Furthermore, a
method for establishing `efficiency' is considered, which takes into account
the variances as well as CPU run times, and the `Double' is significantly more
`efficient' compared to the `Independent' algorithm in most cases.
