Flow of diffeomorphisms for SDEs with unbounded H
By Franco Flandoli, Massimiliano Gubinelli, Enrico Priola. 2009
70 citations recorded by the source corpus.
Abstract We consider a SDE with a smooth multiplicative non-degenerate noise and a possibly unbounded Holder continuous drift term. We prove the 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.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Finance
View Paper: https://www.semanticscholar.org/paper/66e83202d8cd335d050292ea069bd4ea277efd47
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In Applied Mathematics
- Christian Olivera
- Wladimir A. P. Neves
- Feng-Yu Wang
- Michael Röckner
- Patrick Cattiaux
- Nathael Gozlan
- Wei Liu
- Arnaud Guillin
In Computational Theory and Mathematics
- Christian Olivera
- Wladimir A. P. Neves
- Feng-Yu Wang
- Wei Liu
- Michael Röckner
- Xing Huang
- Wei David Liu
In Finance
- Christian Olivera
- Wladimir A. P. Neves
- Feng-Yu Wang
- Michael Röckner
- Wei Liu
- Xing Huang
- Xicheng Zhang
- Panpan Ren
Citations in the corpus
- Wellposedness for stochastic continuity equations with Ladyzhenskaya–Prodi–Serrin condition (2013, background): “Indeed, from Theorem 7 in [13], if b is Hölder not necessarily bounded, then Xt is a Hölder continuous stochastic flow of diffeomorphisms.”
- Gradient estimates and applications for SDEs in Hilbert space with multiplicative noise and Dini continuous drift (2014, methodology): “Note that when b is Hölder continuous and H is finite-dimensional, the (log) Harnack inequalities have been established recently in [14] using the regularization transform of [10, 11].”