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common to treat small jumps of Lévy processes as Wiener noise and to approximate its marginals by a Gaussian results that allow to quantify the goodness of this approximation according to a given metric are rare statistical models converges to zero then no test can be constructed to distinguish the two models and asymptotically equally informative. We provide a Gaussian approximation for the small jumps of Lévy processes in Non-asymptotic bounds for the total variation distance between n discrete observations of small jumps of a Lévy process Total variation distance for discretely observed Lévy processes: a Gaussian approximation of the small
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