We consider a SDE with a smooth multiplicative non-degenerate noise and a possibly unbounded Hölder continuous drift term. We prove the existence of a global flow of diffeomorphisms by means of a special transformation of the drift of Itô–Tanaka type. The proof requires non-standard elliptic estimates in Hölder 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.
Flow of diffeomorphisms for SDEs with unboundedHölder continuous drift
PRIOLA, Enrico
2010-01-01
Abstract
We consider a SDE with a smooth multiplicative non-degenerate noise and a possibly unbounded Hölder continuous drift term. We prove the existence of a global flow of diffeomorphisms by means of a special transformation of the drift of Itô–Tanaka type. The proof requires non-standard elliptic estimates in Hölder 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.
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