REMARKS ON FÖLLMER’S PATHWISE ITÔ CALCULUS

Hirai, Yuki

doi:https://doi.org/10.18910/73360

REMARKS ON FÖLLMER’S PATHWISE ITÔ CALCULUS

Hirai, Yuki

Osaka Journal of Mathematics, 2019, 56(3), 631-660

アクセス数:190件（2025-07-19 08:17 集計）

固定URL: https://doi.org/10.18910/73360

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タイトル	REMARKS ON FÖLLMER’S PATHWISE ITÔ CALCULUS
著者	著者名 Hirai, Yuki
抄録	We extend some results about Föllmer’s pathwise Itô calculus that have only been derived for continuous paths to càdlàg paths with quadratic variation. We study some fundamental properties of pathwise Itô integrals with respect to càdlàg integrators, especially associativity and the integration by parts formula. Moreover, we study integral equations with respect to pathwise Itô integrals. We prove that some classes of integral equations, which can be explicitly solved in the usual stochastic calculus, can also be solved within the framework of Föllmer’s calculus.
出版者	Osaka University and Osaka City University, Departments of Mathematics
収録物名	Osaka Journal of Mathematics
巻(号)	56(3)
ページ	631-660
刊行年月	2019-07
言語	英語
ハンドルURL	https://hdl.handle.net/11094/73360
DOI	https://doi.org/10.18910/73360
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 56, Number 3 （2019-7）

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. 2019, 56(3), p. 631-660
DC.title	REMARKS ON FÖLLMER’S PATHWISE ITÔ CALCULUS
DC.creator	Hirai, Yuki
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	2019-07
DCTERMS.abstract	We extend some results about Föllmer’s pathwise Itô calculus that have only been derived for continuous paths to càdlàg paths with quadratic variation. We study some fundamental properties of pathwise Itô integrals with respect to càdlàg integrators, especially associativity and the integration by parts formula. Moreover, we study integral equations with respect to pathwise Itô integrals. We prove that some classes of integral equations, which can be explicitly solved in the usual stochastic calculus, can also be solved within the framework of Föllmer’s calculus.
DC.identifier	10.18910/73360
DC.format	73360
citation_title	REMARKS ON FÖLLMER’S PATHWISE ITÔ CALCULUS
citation_author	Hirai, Yuki
citation_publisher	Osaka University and Osaka City University, Departments of Mathematics
citation_language	英語
citation_date	2019-07
citation_journal_title	Osaka Journal of Mathematics
citation_volume	56
citation_issue	3
citation_firstpage	631
citation_lastpage	660
citation_public_url	https://hdl.handle.net/11094/73360
citation_doi_detail	10.18910/73360
citation_doi	https://doi.org/10.18910/73360

REMARKS ON FÖLLMER’S PATHWISE ITÔ CALCULUS

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