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- ItemRegularization of statistical inverse problems and the Bakushinskii veto(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Becker, SaskiaLiteraturverz. In the deterministic context Bakushinskiui's theorem excludes the existence of purely data driven convergent regularization for ill-posed problems. We will prove in the present work that in the statistical setting we can either construct a counter example or develop an equivalent formulation depending on the considered class of probability distributions. Hence, Bakushinskiui's theorem does not generalize to the statistical context, although this has often been assumed in the past. To arrive at this conclusion, we will deduce from the classic theory new concepts for a general study of statistical inverse problems and perform a systematic clarification of the key ideas of statistical regularization
- ItemThe enhanced Sanov theorem and propagation of chaos(Amsterdam [u.a.] : Elsevier, 2017) Deuschel, Jean-Dominique; Friz, Peter K.; Maurelli, Mario; Slowik, MartinWe establish a Sanov type large deviation principle for an ensemble of interacting Brownian rough paths. As application a large deviations for the (-layer, enhanced) empirical measure of weakly interacting diffusions is obtained. This in turn implies a propagation of chaos result in a space of rough paths and allows for a robust analysis of the particle system and its McKean–Vlasov type limit, as shown in two corollaries.