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.

翻译：受热辐射输运方程的启发，我们考虑在时空域中经历碰撞的粒子，并提出一种采样其逃逸时间、空间位置和方向的方法。该过程的第一步是估计在退出域的概率过高之前可以安全进行多少次基本碰撞；然后将这些碰撞聚合为单次运动。该方法不使用任何模型，也不依赖任何特定的参数体系。我们在正态近似条件下及无近似条件下均给出了理论结果，并在文献中的若干基准测试上验证了该方法。结果证实了理论预测，并表明该方案是采样粒子逃逸分布的一种高效方法。