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In this article a stochastic particle system approximation to the parametricsensitivity in the Smoluchowski coagulation equation is introduced. Theparametric sensitivity is the derivative of the solution to the equation withrespect to some parameter, where the coagulation kernel depends on thisparameter. It is proved that the particle system converges weakly to thesensitivity as the number of particles N increases. A Monte Carlo algorithm isdeveloped and variance reduction techniques are applied. Numerical experimentsare conducted for two kernels: the additive kernel and one which has been usedfor studying soot formation in a free molecular regime. It is shown empiricallythat the techniques for variance reduction are indeed very effective and thatthe order of convergence is O(1/N). The algorithm is then compared to analgorithm based on a finite difference approximation to the sensitivity and itis found that the variance of the sensitivity estimators are considerably lowerthan that for the finite difference approach. Furthermore, two methods ofestablishing `efficiency' are considered and the new algorithm is found to besignificantly more efficient.

A Stochastic Algorithm for Parametric Sensitivity in Smoluchowski's Coagulation Equation