Da Prato, G, Flandoli, F, Röckner, M et al. (1 more author) (2016) Strong uniqueness for SDEs in Hilbert spaces with nonregular drift. Annals of Probability, 44 (3). pp. 1985-2023. ISSN 0091-1798
Abstract
We prove pathwise uniqueness for a class of stochastic differential equations (SDE) on a Hilbert space with cylindrical Wiener noise, whose non-linear drift parts are sums of the subdifferential of a convex function and a bounded part. This generalizes a classical result by one of the authors to infinite dimensions. Our results also generalize and improve recent results by N. Champagnat and P. E. Jabin, proved in finite dimensions, in the case where their diffusion matrix is constant and non-degenerate and their weakly differentiable drift is the (weak) gradient of a convex function. We also prove weak existence, hence obtain unique strong solutions by the Yamada-Watanabe theorem. The proofs are based in part on a recent maximal regularity result in infinite dimensions, the theory of quasi-regular Dirichlet forms and an infinite dimensional version of a Zvonkin-type transformation. As a main application we show pathwise uniqueness for stochastic reaction diffusion equations perturbed by a Borel measurable bounded drift. Hence such SDE have a unique strong solution.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
Copyright, Publisher and Additional Information: | © 2016 Institute of Mathematical Statistics. Reproduced in accordance with the publisher's self-archiving policy. |
Keywords: | Pathwise uniqueness; stochastic differential equations on Hilbert spaces; stochastic PDEs, maximal regularity on infinite dimensional spaces, (classical) Dirichlet forms, exceptional sets |
Dates: |
|
Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Statistics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 16 Oct 2015 11:47 |
Last Modified: | 27 Aug 2020 14:13 |
Published Version: | http://dx.doi.org/10.1214/15-AOP1016 |
Status: | Published |
Publisher: | Institute of Mathematical Statistics |
Identification Number: | 10.1214/15-AOP1016 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:85672 |