标题： Wasserstein收敛速率用于随机粒子近似玻尔兹曼模型 显示英文标题

标题： Wasserstein convergence rates for stochastic particle approximation of Boltzmann models

摘要： 我们建立了基于Nanbu型蒙特卡罗方案的随机粒子近似的定量收敛速率，该方案应用于一类广泛的碰撞动力学模型。 使用耦合技术和Wasserstein-1（Kantorovich-Rubinstein）度量中的稳定性估计，我们推导出反映模型非线性相互作用结构的精确误差界限。 我们的框架包括经典的Nanbu蒙特卡罗方法以及最近发展的时滞放松蒙特卡罗方法。 这些结果弥合了概率粒子近似与确定性数值误差分析之间的差距，并为Boltzmann型方程的蒙特卡罗方法的收敛理论提供了统一的观点。 作为副产品，我们还获得了大量Boltzmann型方程解的存在性和唯一性。 显示英文摘要

摘要： We establish quantitative convergence rates for stochastic particle approximation based on Nanbu-type Monte Carlo schemes applied to a broad class of collisional kinetic models. Using coupling techniques and stability estimates in the Wasserstein-1 (Kantorovich-Rubinstein) metric, we derive sharp error bounds that reflect the nonlinear interaction structure of the models. Our framework includes classical Nanbu Monte Carlo method and more recent developments as Time Relaxed Monte Carlo methods. The results bridge the gap between probabilistic particle approximations and deterministic numerical error analysis, and provide a unified perspective for the convergence theory of Monte Carlo methods for Boltzmann-type equations. As a by-product, we also obtain existence and uniqueness of solutions to a large class of Boltzmann-type equations.