Model free collision aggregation for the computation of escape distributions

Motivated by a heat radiative transport equation, we consider a particle undergoing collisions in a space-time domain and propose a method to sample its escape time, space and direction from the domain. The first step of the procedure is an estimation of how many elementary collisions is safe to take before chances of exiting the domain are too high; then these collisions are aggregated into a single movement. The method does not use any model nor any particular regime of parameters. We give theoretical results both under the normal approximation and without it and test the method on some benchmarks from the literature. The results confirm the theoretical predictions and show that the proposal is an efficient method to sample the escape distribution of the particle.