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The paper is focused on justification of a statistical modelling algorithm for solution of the nonlinear kinetic Boltzmann equation on the base of a projection method. Hermite functions are used as an orthonormal basis. The error of approximation of a function by a partial sum of Hermite functions series is estimated in the  L  2  norm. The estimates are compared for two variants of the projection method in the case of solutions to the homogeneous gas relaxation problem with a known solution.

Two variants of Monte Carlo projection method for numerical solution of nonlinear Boltzmann equation