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In this paper we present the initial results in our development of Distributional DSMC (DDSMC) methods. By modifying Nanbu's method to allow distributed velocities, we have shown that DSMC methods are not limited to convergence in probability measure alone, but can achieve strong convergence for L 1 solutions of the Boltzmann equation and pointwise convergence for bounded solutions. We also present an initial attempt at a general distributional method and apply these methods to the Bobylev,doi:10.1063/1.3562668 fatcat:ocxmxqfgubdtvd56n6ndvpj5jm