  We consider a SDE with a smooth multiplicative non-degenerate noise and a
possibly unbounded Holder continuous drift term. We prove existence of a global
flow of diffeomorphisms by means of a special transformation of the drift of
Ito-Tanaka type. The proof requires non-standard elliptic estimates in Holder
spaces. As an application of the stochastic flow, we obtain a
Bismut-Elworthy-Li type formula for the first derivatives of the associated
diffusion semigroup.
