Development of stochastic analysis toward to organic connections between local structures and global structures

• Project/Area Number: 18740070
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Basic analysis
• Research Institution: Kyoto University
• Principal Investigator: HINO Masanori Kyoto University, 大学院・情報学研究科, 准教授 (40303888)
• Project Period (FY): 2006 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥3,830,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥330,000); Fiscal Year 2008: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2007: ¥1,200,000 (Direct Cost: ¥1,200,000); Fiscal Year 2006: ¥1,200,000 (Direct Cost: ¥1,200,000)
• Keywords: 確率解析 / 無限次元空間 / フラクタル / 自己相似集合 / ディリクレ形式 / 抽象ウィナー空間 / 有界変動関数 / エネルギー測度 / Dirichlet形式 / 拡散過程 / 指数 / マルチンゲール次元 / 微分構造 / 抽象Wiener空間 / Hausdorff測度 / 部分積分公式 / Skorohod表現 / 対称拡散過程 / 経路空間 / Skorokhod表現

Research Abstract

経路空間を典型例とする無限次元空間や, フラクタル集合などの複雑な空間において, 特に局所構造や大域構造に着目した確率解析の理論を展開した。滑らかな空間に適用できる様々の理論が利用できないため, このような研究には新たな解析手段を開発することが必要となる。今回の研究においては無限次元空間, フラクタル集合それぞれにおいて順当な問題をいくつか設定し, その解答を与えることを通じて新たな理論の展開を行った。

Research Products

• [Journal Article] Reflecting Ornstein-Uhlenbeck processes on pinned path spaces, Proceedings of RIMS Workshop on Stochastic Analysis and Applications (2008)
  • Author(s): Masanori Hino and Hiroto Uchida
  • Journal Title: Res. Inst. Math. Sci. (RIMS) RIMS Kokyuroku Bessatsu, B6 Pages: 111-128
  • NAID: 110006487699
  • Peer Reviewed
• [Journal Article] Martingale dimensions for fractals (2008)
  • Author(s): Masanori Hino
  • Journal Title: Annals of Probability Vol. 36 Pages: 971-991
  • Peer Reviewed
• [Journal Article] Martingale dimensions for fractals (2008)
  • Author(s): Masanori Hino
  • Journal Title: Annals of Probability Vol.36 Pages: 971-991
  • Peer Reviewed
• [Journal Article] Reflecting Ornstein-Uhlenbeck processes on pinned pathspaces (2008)
  • Author(s): Masanori Hino and Hiroto Uchida
  • Journal Title: Proceedings of RIMS Workshop on Stochastic Analysis and Applications, RIMS Kokyuroku Bessatsu, Res. Inst. Math. Sci. B6 Pages: 111-128
  • Peer Reviewed
• [Journal Article] A trace theorem for Dirichlet forms on fractals (2006)
  • Author(s): Masanori Hino and Takashi Kumagai
  • Journal Title: Journal of Functional Analysis Vol. 238 Pages: 578-611
  • Peer Reviewed
• [Journal Article] On singularity of energy measures on self-similar sets II (2006)
  • Author(s): Masanori Hino and Kenji Nakahara
  • Journal Title: Bulletin of the London Mathematical Society Vol. 38 Pages: 1019-1032
  • Peer Reviewed
• [Journal Article] A trace theorem for Dirichlet forms on fractals (2006)
  • Author(s): Masanori Hino, Takashi Kumagai
  • Journal Title: Journal of Functional Analysis 238 Pages: 578-611
• [Journal Article] On singularity of energy measures on self-similar sets II (2006)
  • Author(s): Masanori Hino, Kenji Nakahara
  • Journal Title: Bulletin of the London Mathematical Society 38 Pages: 1019-1032
• [Presentation] Energy measures and derivatives on some fractals (2008)
  • Author(s): Masanori Hino
  • Organizer: 日独共同研究Stochastic Analysis and Applications 2008
  • Place of Presentation: 西新プラザ(福岡県)
  • Year and Date: 2008-09-09
• [Presentation] Energy measures and derivatives on p. c. f. self-similar sets (2008)
  • Author(s): Masanori Hino
  • Organizer: 3rd Conference on Analysis and Probability on Fractals
  • Place of Presentation: Cornell University(米国)
  • Year and Date: 2008-06-13
• [Presentation] Sets of finite perimeter and Hausdorff measures on the Wiener space (2008)
  • Author(s): Masanori Hino
  • Organizer: 2nd International Conference on Stochastic Analysis and Its Applications
  • Place of Presentation: Seoul National University(韓国)
  • Year and Date: 2008-05-31
• [Presentation] Energy measures and derivatives on some fractals (2008)
  • Author(s): 日野正訓
  • Organizer: 日独共同研究 Stochastic Analysis and Applications 2008
  • Place of Presentation: 西新プラザ(福岡市)
• [Presentation] Energy measures and derivatives on p. c. f. self-similar sets (2008)
  • Author(s): 日野正訓
  • Organizer: 3rd Conference on Analysis and Probability on Fractals
  • Place of Presentation: Cornell University
• [Presentation] Sets of finite perimeter and Hausdorff measures on the Wiener space (2008)
  • Author(s): 日野正訓
  • Organizer: 2nd International Conference on Stochastic Analysis and Its Applications
  • Place of Presentation: Seoul National University, Korea
• [Presentation] Reflecting Ornstein-Uhlenbeck Processes on Path Spaces (2006)
  • Author(s): 日野正訓
  • Organizer: Stochastic Analysis and Applications
  • Place of Presentation: Kyoto University
• [Presentation] Martingale dimensions for fractals (2006)
  • Author(s): 日野正訓
  • Organizer: Mathematics on Fractals 2006
  • Place of Presentation: Kyoto University
• [Presentation] Reflecting Ornstein-Uhlenbeck Processes on Path Spaces (2006)
  • Author(s): 日野正訓
  • Organizer: International Conference on Stochastic Analysis and Its Applications
  • Place of Presentation: University of Washington