On Sobolev rough paths
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Date
2021-05-01
Publication Type
Journal Article
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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.
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published
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Journal / series
Volume
497 (1)
Pages / Article No.
124876
Publisher
Elsevier
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Subject
Itô–Lyons map; Sobolev space; Rough differential equation; Rough path
Organisational unit
03845 - Teichmann, Josef / Teichmann, Josef
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Funding
163014 - Regularity structures in mathematical Finance (SNF)