On Sobolev rough paths
dc.contributor.author
Liu, Chong
dc.contributor.author
Prömel, David J.
dc.contributor.author
Teichmann, Josef
dc.date.accessioned
2021-01-11T12:04:38Z
dc.date.available
2021-01-03T03:39:11Z
dc.date.available
2021-01-11T12:04:38Z
dc.date.issued
2021-05-01
dc.identifier.issn
0022-247X
dc.identifier.issn
1096-0813
dc.identifier.other
10.1016/j.jmaa.2020.124876
en_US
dc.identifier.uri
http://hdl.handle.net/20.500.11850/458884
dc.description.abstract
We introduce the space of rough paths with Sobolev regularity and the corresponding concept of controlled Sobolev paths. Based on these notions, we study rough path integration and rough differential equations. As main result, we prove that the solution map associated to differential equations driven by rough paths is a locally Lipschitz continuous map on the Sobolev rough path space for any arbitrary low regularity α and integrability p provided α > 1/p. © 2020 Elsevier Inc.
en_US
dc.language.iso
en
en_US
dc.publisher
Elsevier
en_US
dc.subject
Itô–Lyons map
en_US
dc.subject
Sobolev space
en_US
dc.subject
Rough differential equation
en_US
dc.subject
Rough path
en_US
dc.title
On Sobolev rough paths
en_US
dc.type
Journal Article
dc.date.published
2020-12-18
ethz.journal.title
Journal of Mathematical Analysis and Applications
ethz.journal.volume
497
en_US
ethz.journal.issue
1
en_US
ethz.journal.abbreviated
J. math. anal. appl.
ethz.pages.start
124876
en_US
ethz.size
21 p.
en_US
ethz.grant
Regularity structures in mathematical Finance
en_US
ethz.identifier.wos
ethz.identifier.scopus
ethz.publication.place
Amsterdam
en_US
ethz.publication.status
published
en_US
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02003 - Mathematik Selbständige Professuren::03845 - Teichmann, Josef / Teichmann, Josef
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02003 - Mathematik Selbständige Professuren::03845 - Teichmann, Josef / Teichmann, Josef
ethz.grant.agreementno
163014
ethz.grant.fundername
SNF
ethz.grant.funderDoi
10.13039/501100001711
ethz.grant.program
Projektförderung in Mathematik, Natur- und Ingenieurwissenschaften (Abteilung II)
ethz.date.deposited
2021-01-03T03:39:26Z
ethz.source
SCOPUS
ethz.eth
yes
en_US
ethz.availability
Metadata only
en_US
ethz.rosetta.installDate
2021-01-11T12:04:47Z
ethz.rosetta.lastUpdated
2022-03-29T04:46:42Z
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true
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