Stochastic Numerics for the Boltzmann Equation

Focusing on stochastic numerical methods, this book provides a mathematical framework for classical direct simulation Monte Carlo (DSMC) techniques applied to rarefied gases, utilizing Markov processes. It also explores the stochastic weighted particle method, an advanced extension of DSMC designed for variance reduction in rare event simulations. The text includes rigorous convergence results and comprehensive numerical studies, making it a valuable resource for understanding and applying these methods in large-scale computations within the applied sciences.