Simulation of coalescence with stratified sampling

We analyze a stratified strategy for numerical integration and for simulation of coalescence. We use random points which are more evenly distributed in the unit cube than usual pseudo-random numbers. They are constructed so that only one point of the set lies in specific sub-intervals of the cube. This property leads to an improved convergence rate for the variance, when they are used for integrating indicator functions. A bound for the variance is proved and assessed through a numerical experiment. We also devise a Monte Carlo algorithm for the simulation of the coagulation equation. We start with an initial population of particles whose sizes are sampled from some initial distribution, and these sizes evolve according to the coalescence dynamics; the random numbers used are the stratified points described above. The results of some numerical experiments show a smaller variance, when compared to a Monte Carlo simulation using plain random samples.