Bias of the Bird type estimator

We consider a system of spatially homogeneous Smoluchowski equations. We will suggest that the coagulation coefficients are finite. Among numerical methods for solving this problem, Monte Carlo algorithms, based on the direct simulation of the coagulation process in a model particle system, play an important role. Note, that the Smoluchowski equations have nearly the same structure, as the Boltzmann equation; so, it is quite natural to use for them the well-developed stochastic algorithms for solving the latter. The present work develops the algorithm constructed by Bird for solving the Boltzmann equation and applied for the Smoluchowski equations.