Stochastic algorithms of the mathematical theory of the spatially inhomogeneous Boltzmann equation for gas mixture

A new mathematically rigorous approach for the particle simulation of the spatially inhomogeneous Boltzmann equation for gas mixture is considered. This approach relies on an approximation of the Boltzmann equation by systems of stochastic differential equations with respect to Poisson measure and has first been suggested by A. V. Skorochod and A. A. Arsen'ev. Stochastic simulation schemes for the Boltzmann equation for gas mixture are considered as the methods of the numerical solution of stochastic equations and are tested on the rarefied gas shock wave problem.