Flow of diffeomorphisms for SDEs with unbounded H\"older continuous drift
Probability
2009-07-22 v1
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.
Keywords
Cite
@article{arxiv.0907.3668,
title = {Flow of diffeomorphisms for SDEs with unbounded H\"older continuous drift},
author = {F. Flandoli and M. Gubinelli and E. Priola},
journal= {arXiv preprint arXiv:0907.3668},
year = {2009}
}
Comments
21 pages