• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Foundations of an anti-symmetric version of Malliavin calculus

Research Project

Project/Area Number 23654056
Research Category

Grant-in-Aid for Challenging Exploratory Research

Allocation TypeMulti-year Fund
Research Field Basic analysis
Research InstitutionRitsumeikan University

Principal Investigator

AKAHORI Jiro  立命館大学, 理工学部, 教授 (50309100)

Project Period (FY) 2011 – 2013
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords反対称マリアバン解析 / クリフォード代数 / フェルミオン / ボゾン化 / タウ関数 / 確率面積 / 佐藤グラスマン多様体 / マリアバン解析
Research Abstract

This project aimed to provide foundations to an anti-symmetric version of Malliavin calculus. As outputs, we obtained the following mathematical results. The first is that we have succeeded to obtain a probabilistic representation of tau functions of KP hierarchy, which fully extends the previous results on KdV one. The second is that we constructed a representation of Clifford algebra on Wiener space. Based on it, we also succeeded to construct a probabilistic Bosonization, which is the third of our main contributions in this project. Other than these, we have also obtained an interesting result on a relation between solitons of KdV equation and the term structure of interest rates in mathematical finance.

Report

(4 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (15 results)

All 2014 2013 2012 2011 Other

All Journal Article (5 results) (of which Peer Reviewed: 4 results,  Open Access: 1 results) Presentation (8 results) (of which Invited: 4 results) Remarks (2 results)

  • [Journal Article] Affine term structure as multi-soliton2014

    • Author(s)
      Hidemi Aihara, Jiro Akahori, and Edouard Grenier
    • Journal Title

      JSIAM Letters

      Volume: 6 Issue: 0 Pages: 17-20

    • DOI

      10.14495/jsiaml.6.17

    • NAID

      130004540626

    • ISSN
      1883-0609, 1883-0617
    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Tau functions of KP solitons realized in Wiener space2013

    • Author(s)
      Hidemi Aihara, Jiro Akahori, Hiroko Fujii, Yasuhumi Nitta
    • Journal Title

      Bulletin of the London Mathematical Society

      Volume: 45/6 Issue: 6 Pages: 1301-1309

    • DOI

      10.1112/blms/bdt056

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] An Algebraic Approach to the Cameron-Martin-Maruyama-Girsano v Formula2013

    • Author(s)
      Jiro Akahori, Takafumi Amaba, Sachiyo Uraguchi
    • Journal Title

      Mathematical Journal of Okayama University

      Volume: 55 Pages: 167-190

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] An Algebraic Approach to the Cameron-Martin-Maruyama-Girsanov Formula2013

    • Author(s)
      Jiro Akahori, Takafumi Amaba, Sachiyo Uraguchi
    • Journal Title

      Mathematical Journal of Okayama University

      Volume: 55 Pages: 167-190

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Tau functions of KP solitons realized in Wiener space2011

    • Author(s)
      Hidemi Aihara, Ji Hiroko Fujii, and Yasuhumi Nitta
    • Journal Title

      arXiv

      Volume: arXiv:1108.0768

    • Related Report
      2011 Research-status Report
  • [Presentation] A Modification of the Fourier Method2014

    • Author(s)
      Jiro Akahori
    • Organizer
      Stochastic Processes and Mathematical Finance
    • Place of Presentation
      関西大学(大阪府)
    • Year and Date
      2014-02-25
    • Related Report
      2013 Final Research Report
  • [Presentation] Algebraic proof of anticipative Girsanov-Maruyama Formula2013

    • Author(s)
      Jiro Akahori
    • Organizer
      The First International Workshop on Quantum Information Theory and Related Topics
    • Place of Presentation
      ダナン市(ベトナム)
    • Year and Date
      2013-08-19
    • Related Report
      2013 Final Research Report
  • [Presentation] Solitons via Stochastic Areas2012

    • Author(s)
      Jiro Akahori
    • Organizer
      Rough Path解析とその周辺
    • Place of Presentation
      名古屋大学(愛知県)
    • Related Report
      2011 Research-status Report
  • [Presentation] A Modification of the Fourier Method

    • Author(s)
      J.Akahori
    • Organizer
      Stochastic Processes and Mathematical Finance
    • Place of Presentation
      関西大学(大阪府)
    • Related Report
      2013 Annual Research Report
  • [Presentation] Algebraic proof of anticipative Girsanov-Maruyama formula

    • Author(s)
      J. Akahori
    • Organizer
      The First International Workshop on Quantum Information Theory and Related Topics
    • Place of Presentation
      Danang, Vietnam
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] An Algebraic Approach to the Ramer-Kusuoka Formula

    • Author(s)
      Jiro Akahori
    • Organizer
      Perspectives in Analysis and Probability. Conference in Honor of Freddy Delbaen
    • Place of Presentation
      チューリッヒ,スイス
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] On a Symmetrization of Diffusion Processes

    • Author(s)
      Jiro Akahori
    • Organizer
      Quantitative Methods in Finance
    • Place of Presentation
      ケアンズ,オーストラリア
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Sato's Grassmanian in Wiener space

    • Author(s)
      Jiro Akahori
    • Organizer
      3rd Monash-Ritsumeikan Symposium on Probability and Related Fields
    • Place of Presentation
      メルボルン,オーストラリア
    • Related Report
      2012 Research-status Report
    • Invited
  • [Remarks] research-db

    • URL

      http://research-db.ritsumei.ac.jp/Profiles/38/0003770/prof_e.html

    • Related Report
      2013 Annual Research Report
  • [Remarks] 立命館大学 研究者学術情報データベース

    • URL

      http://research-db.ritsumei.ac.jp/Profiles/38/0003770/profile.html

    • Related Report
      2012 Research-status Report

URL: 

Published: 2011-08-05   Modified: 2019-07-29  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi