F. Flandoli, M. Gubinelli and E. Priola
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.
F. Flandoli, M. Gubinelli and E. Priola. Flow of diffeomorphisms for SDEs with unbounded Hölder continuous drift. Papers of Massimiliano Gubinelli, 2009, version 1. https://mgubi.org/papers/paper/sde-flows-unbounded-drift/
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