The theory of rough paths via one-forms and the extension of an argument of Schwartz to rough differential equations

• Lyons Terry J.

  The Oxford-Man Institute, University of Oxford

• Yang Danyu

  The Oxford-Man Institute, University of Oxford

抄録

We give an overview of the recent approach to the integration of rough paths that reduces the problem to an inhomogeneous analogue of the classical Young integration [13]. As an application, we extend an argument of Schwartz [11] to rough differential equations, and prove the existence, uniqueness and continuity of the solution, which is applicable when the driving path takes values in nilpotent Lie group or Butcher group.

収録刊行物

• Ｊｏｕｒｎａｌ　ｏｆ　ｔｈｅ　Ｍａｔｈｅｍａｔｉｃａｌ　Ｓｏｃｉｅｔｙ　ｏｆ　Ｊａｐａｎ

  Ｊｏｕｒｎａｌ　ｏｆ　ｔｈｅ　Ｍａｔｈｅｍａｔｉｃａｌ　Ｓｏｃｉｅｔｙ　ｏｆ　Ｊａｐａｎ 67 (4), 1681-1703, 2015

  一般社団法人 日本数学会

キーワード

• rough paths theory
• Young integral
• integrable one-forms
• universal limit theorem

詳細情報

• CRID: 1390282680092009728
• NII論文ID: 130005108952
• NII書誌ID: AA0070177X
• DOI: 10.2969/jmsj/06741681
• ISSN: 18811167
• ISSN: 18812333
• ISSN: 00255645
• NDL書誌ID: 026817713
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I026817713
• 本文言語コード: en
• データソース種別:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
• 抄録ライセンスフラグ: 使用不可