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We consider a multivariate Lévy process given by the sum of a Brownian motion with drift and an independent time-homogeneous pure jump process governed by a Lévy density. We assume that observation of a sample path takes place on an equidistant discrete time grid. Following Grenander's method of sieves, we construct families of non-parametric projection estimators for the restriction of a Lévy density to bounded sets away from the origin. Moreover, we introduce a data-driven penalisationdoi:10.1080/10485252.2011.581375 fatcat:jaaz7ht6dfde5kbifzvfwrtswa