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Flow of diffeomorphisms for SDEs with unbounded Hölder continuous drift

✍ Scribed by F. Flandoli; M. Gubinelli; E. Priola

Publisher
Elsevier Science
Year
2010
Tongue
French
Weight
204 KB
Volume
134
Category
Article
ISSN
0007-4497

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✦ Synopsis

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.

📜 SIMILAR VOLUMES

Hölder continuity conditions for the sol
Hölder continuity conditions for the solvability of Dirichlet problems involving functionals with free discontinuities
✍ F.A Lops; F Maddalena; S Solimini 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 272 KB

The paper deals with the problem of minimizing a free discontinuity functional under Dirichlet boundary conditions. An existence result was known so far for C 1 (∂ ) boundary data û. We show here that the same result holds for û ∈ C 0,µ (∂ ) if µ > 1 2 and it cannot be extended to cover the case µ =