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For a class of piecewise deterministic Markov processes we introduce astochastic calculus which is a certain non-Gaussian counterpart to theclassical Malliavin calculus. As an application we investigate the regularityof densities of $N$-particle Boltzmann type processes at time $t>0$.

Elements of the Stochastic Calculus for a Class of Boltzmann type processes and Application to Regularity of Densities