- Journal Article
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. Show more
Journal / seriesJournal of Mathematical Analysis and Applications
Pages / Article No.
SubjectItô–Lyons map; Sobolev space; Rough differential equation; Rough path
Organisational unit03845 - Teichmann, Josef / Teichmann, Josef
163014 - Regularity structures in mathematical Finance (SNF)
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