Flow of diffeomorphisms for SDEs with unbounded Hölder continuous drift. (English) Zbl 1198.60023
Summary: 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.
MSC:
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
Keywords:
global flow of diffeomorphisms; drift of Itô-Tanaka type; Bismut-Elworthy-Li type formula; associated diffusion semigroupReferences:
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