LIPSCHITZ-STABILITY OF CONTROLLED ROUGH PATHS AND ROUGH DIFFERENTIAL EQUATIONS

Boedihardjo, Horatio; Geng, Xi

doi:https://doi.org/10.18910/88491

LIPSCHITZ-STABILITY OF CONTROLLED ROUGH PATHS AND ROUGH DIFFERENTIAL EQUATIONS

Boedihardjo, Horatio; Geng, Xi

Osaka Journal of Mathematics, 2022, 59(3), 653-682

アクセス数:164件（2026-07-19 22:00 集計）

固定URL: https://doi.org/10.18910/88491

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タイトル	LIPSCHITZ-STABILITY OF CONTROLLED ROUGH PATHS AND ROUGH DIFFERENTIAL EQUATIONS
著者	著者名 Boedihardjo, Horatio
著者	著者名 Geng, Xi
抄録	We provide an account for the existence and uniqueness of solutions to rough differential equations in infinite dimensions under the framework of controlled rough paths. The case when the driving path is α-Hölder continuous for α > 1/3 is widely available in the literature. In its extension to the case when α ? 1/3, the main challenge and missing ingredient is to show that controlled rough paths are closed under composition with Lipschitz transformations. Establishing such a property precisely, which has a strong algebraic nature, is a main purpose of the present article.
出版者	Osaka University and Osaka City University, Departments of Mathematics
収録物名	Osaka Journal of Mathematics
巻(号)	59(3)
ページ	653-682
刊行年月	2022-07
言語	英語
ハンドルURL	https://hdl.handle.net/11094/88491
DOI	https://doi.org/10.18910/88491
PISSN	00306126
NCID	AA00765910
アクセス権	open access
出版タイプ	Version of Record
カテゴリ	紀要論文 Departmental Bulletin Paper
カテゴリ	Osaka Journal of Mathematics / Volume 59, Number 3 （2022-7）

資源タイプ	紀要論文
ローカル資源タイプ	紀要論文
DCMI資源タイプ	text
DCTERMS.bibliographicCitation	Osaka Journal of Mathematics. 2022, 59(3), p. 653-682
DC.title	LIPSCHITZ-STABILITY OF CONTROLLED ROUGH PATHS AND ROUGH DIFFERENTIAL EQUATIONS
DC.creator	Boedihardjo, Horatio
DC.creator	Geng, Xi
DC.publisher	Osaka University and Osaka City University, Departments of Mathematics
DC.language' scheme='DCTERMS.RFC1766	英語
DC.type' scheme='DCTERMS.DCMIType	text
DCTERMS.issued' scheme='DCTERMS.W3CDTF	2022-07
DCTERMS.abstract	We provide an account for the existence and uniqueness of solutions to rough differential equations in infinite dimensions under the framework of controlled rough paths. The case when the driving path is α-Hölder continuous for α > 1/3 is widely available in the literature. In its extension to the case when α ? 1/3, the main challenge and missing ingredient is to show that controlled rough paths are closed under composition with Lipschitz transformations. Establishing such a property precisely, which has a strong algebraic nature, is a main purpose of the present article.
DC.identifier	10.18910/88491
DC.format	88491
citation_title	LIPSCHITZ-STABILITY OF CONTROLLED ROUGH PATHS AND ROUGH DIFFERENTIAL EQUATIONS
citation_author	Boedihardjo, Horatio
citation_author	Geng, Xi
citation_publisher	Osaka University and Osaka City University, Departments of Mathematics
citation_language	英語
citation_date	2022-07
citation_journal_title	Osaka Journal of Mathematics
citation_volume	59
citation_issue	3
citation_firstpage	653
citation_lastpage	682
citation_public_url	https://hdl.handle.net/11094/88491
citation_doi_detail	10.18910/88491
citation_doi	https://doi.org/10.18910/88491

LIPSCHITZ-STABILITY OF CONTROLLED ROUGH PATHS AND ROUGH DIFFERENTIAL EQUATIONS

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