Metadata only
Datum
2021-05-01Typ
- Journal Article
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. Mehr anzeigen
Publikationsstatus
publishedExterne Links
Zeitschrift / Serie
Journal of Mathematical Analysis and ApplicationsBand
Seiten / Artikelnummer
Verlag
ElsevierThema
Itô–Lyons map; Sobolev space; Rough differential equation; Rough pathOrganisationseinheit
03845 - Teichmann, Josef / Teichmann, Josef
Förderung
163014 - Regularity structures in mathematical Finance (SNF)