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Rough path theory and its application to probability theory

Research Project

Project/Area Number 19740064
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Basic analysis
Research InstitutionTokyo Institute of Technology

Principal Investigator

INAHAMA Yuzuru  Tokyo Institute of Technology, 大学院・理工学研究科, 助教 (80431998)

Project Period (FY) 2007 – 2008
Project Status Completed (Fiscal Year 2008)
Budget Amount *help
¥2,170,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥270,000)
Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2007: ¥1,000,000 (Direct Cost: ¥1,000,000)
Keywords確率解析 / 無限次元解析 / ラフパス理論 / 確率微分方程式 / 伊藤写像 / 大偏差原理 / ラプラス近似 / 漸近展開 / 確率論 / 確率テーラー展開 / ループ空間
Research Abstract

研究成果の概要 : ラフパス理論とは、伊藤清の創設した通常の確率微分方程式論を「非ランダム化」するものであり、その結果、微分方程式の入力パスを出力パスに対応させる伊藤写像は連続写像になる。本研究においては、この伊藤写像にたいしてある種のテーラー展開を試み、それを利用して確率論の有名な漸近定理(大偏差原理やラプラス近似)を示した。またこの種の定理をバナッハ空間に値をとるプロセスに適用すると、通常の確率微分方程式論では証明できていない例が示せることがわかった。現在は、この種の定理をいろいろな場合に拡張中である。

Report

(3 results)
  • 2008 Annual Research Report   Final Research Report ( PDF )
  • 2007 Annual Research Report
  • Research Products

    (14 results)

All 2009 2008 2007

All Journal Article (7 results) (of which Peer Reviewed: 7 results) Presentation (7 results)

  • [Journal Article] On the Laplace-type asymptotics and the stochastic Taylor expansion for It\^o functionals of Brownian rough paths2008

    • Author(s)
      Yuzuru Inahama & Hiroshi Kawabi
    • Journal Title

      {\it RIMS Kokyuroku Bessatsu} {\bf B6}

      Pages: 139-152

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the Laplace-type asymptotics and the stochastic Taylor expansion for It\^o functionals of Brownian rough path2008

    • Author(s)
      Yuzuru Inahama
    • Journal Title

      RIMS Kokyuroku Bessats B6

      Pages: 139-152

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On asymptotics of Banach space-valued It\~{o} functionals of Brownian rough paths2007

    • Author(s)
      Yuzuru Inahama & Hiroshi Kawabi
    • Journal Title

      Stochastic Analysis and Applications -The Abel symposium 2005, Stockholm, Springer

      Pages: 415-434

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic expansions for the Laplace approximations for It\^{o} functionals ofBrownian rough paths2007

    • Author(s)
      Yuzuru Inahama & Hiroshi Kawabi
    • Journal Title

      J. Funct. Anal. {\bf 243} no. 1

      Pages: 270-322

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic expansions for the Laplace approximations for It\^{o} functionals of Brownian rough paths2007

    • Author(s)
      Yuzuru lnahama, Hiroshi Kawabi
    • Journal Title

      J. Funct. Anal. 243

      Pages: 270-322

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On asymptotics of Banach space-valued It\-{o} functionals of Brownian rough paths2007

    • Author(s)
      Yuzuru lnahama, Hiroshi Kawabi
    • Journal Title

      The Abel symposium 2005, Stockholm, Springer

      Pages: 415-434

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the Laplace-type asymptotics and the stochastic Taylor expansion for lt\^o functionals of Brownian rough paths2007

    • Author(s)
      Yuzuru lnahama, Hiroshi Kawabi
    • Journal Title

      RIMS Kokyuroku Bessatsu B6

      Pages: 139-152

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Presentation] Rough path analysis for an infinite dimensional diffusion2009

    • Author(s)
      稲浜譲
    • Organizer
      日本数学会 統計数学分科会 特別講演
    • Place of Presentation
      東京大学
    • Year and Date
      2009-03-26
    • Related Report
      2008 Final Research Report
  • [Presentation] A stochastic Taylor-like expansion in the rough path theory.2008

    • Author(s)
      Yuzuru Inahama
    • Organizer
      The 1st MSJ-SI (The Mathematical Society of Japan, Seasonal Institute), Probabilistic Approach to Geometry
    • Place of Presentation
      京都大学
    • Year and Date
      2008-07-31
    • Related Report
      2008 Final Research Report
  • [Presentation] A stochastic Taylor-like expansion in the rough path theory2008

    • Author(s)
      Yuzuru Inahama
    • Organizer
      The 1st MSJ-SI (The Mathematical Society of Japan, Seasonal Ins titute), Probabilistic Approach to Geometr
    • Place of Presentation
      京都大学
    • Year and Date
      2008-07-31
    • Related Report
      2008 Annual Research Report
  • [Presentation] A stochastic Taylor-like expansion in the rough path theory.2007

    • Author(s)
      稲浜譲
    • Organizer
      確率解析とその周辺
    • Place of Presentation
      東京工業大学
    • Year and Date
      2007-11-24
    • Related Report
      2008 Final Research Report
  • [Presentation] A stochastic Taylor-like expansion in the rough path theory2007

    • Author(s)
      稲浜 譲
    • Organizer
      確率論とその周辺
    • Place of Presentation
      東京工業大学
    • Year and Date
      2007-11-24
    • Related Report
      2007 Annual Research Report
  • [Presentation] A stochastic Taylor-like expansion in the rough path theory.2007

    • Author(s)
      Yuzuru Inahama
    • Organizer
      Stochastic calculus on manifolds, graphs, and random structures
    • Place of Presentation
      University of Bonn
    • Year and Date
      2007-10-08
    • Related Report
      2008 Final Research Report
  • [Presentation] A stochastic Tay1or-like expansion in the rough path theory2007

    • Author(s)
      Yuzuru Inahama
    • Organizer
      Stochastic Calculus on manifolds, graphs, and Random structures
    • Place of Presentation
      Univ. Bonn
    • Year and Date
      2007-10-08
    • Related Report
      2007 Annual Research Report

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Published: 2007-04-01   Modified: 2016-04-21  

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