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We consider a SDE with a smooth multiplicative non-degenerate noise and apossibly unbounded Holder continuous drift term. We prove existence of a globalflow of diffeomorphisms by means of a special transformation of the drift ofIto-Tanaka type. The proof requires non-standard elliptic estimates in Holderspaces. As an application of the stochastic flow, we obtain aBismut-Elworthy-Li type formula for the first derivatives of the associateddiffusion semigroup.

Flow of diffeomorphisms for SDEs with unbounded H\"older continuous drift