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arXiv · 0907.3668

Flow of diffeomorphisms for SDEs with unbounded Hölder continuous drift

F. Flandoli·M. Gubinelli·E. Priola
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Abstract

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.

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F. Flandoli, M. Gubinelli, E. Priola. 2009-07-21. Flow of diffeomorphisms for SDEs with unbounded Hölder continuous drift. https://arxiv.org/abs/0907.3668

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