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Study on basic properties of the noncausal stochastic differential equations

Research Project

Project/Area Number 26400152
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Basic analysis
Research InstitutionRitsumeikan University

Principal Investigator

OGAWA SHIGEYOSHI  立命館大学, 薬学部, 非常勤講師 (80101137)

Co-Investigator(Kenkyū-buntansha) 植村 英明  愛知教育大学, 教育学部, 教授 (30203483)
Project Period (FY) 2014-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords非因果的確率解析 / 確率積分 / 確率微分方程式 / 確率偏微分方程式 / 確率フーリエ変換 / 非因果的システム / 確率モデル / 非因果的積分 / フレドホルム型確率積分方程式 / 非線形熱方程式 / 確率フーリエ係数 / 確率論 / 確率解析 / Ogawa Integral / 非因果的確率微積分方程式 / ブラウン粒子方程式 / 非因果的確率システム
Outline of Final Research Achievements

The main subject of the research is "the study on the basic properties of the noncausal stochastic functional equations, including the stochastic differential, stochastic partial differential, and integral equations" As the models of those noncausal equations we have chosen those equations that appear in the application domain of mathematical physics and finances. On each case, we have achieved almost every aim that we listed as main problems. As the result, we have published 9 articles and made about 19 lectures in the mathematical meeting and conferences.

Report

(5 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Research-status Report
  • 2015 Research-status Report
  • 2014 Research-status Report
  • Research Products

    (25 results)

All 2018 2017 2016 2015 2014

All Journal Article (6 results) (of which Int'l Joint Research: 3 results,  Peer Reviewed: 6 results,  Open Access: 3 results) Presentation (18 results) (of which Invited: 12 results) Book (1 results)

  • [Journal Article] Some aspects of strong inversion formulas of an SFT2018

    • Author(s)
      OGAWA,S. & UEMURA,H.
    • Journal Title

      JJAIM Japan Journal of Industrial and Applied Mathematics

      Volume: 35 - 1 Issue: 1 Pages: 373-390

    • DOI

      10.1007/s13160-017-0295-3

    • NAID

      210000176127

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Regularity of Gaussian processes on Dirichlet spaces2018

    • Author(s)
      OGAWA,S., Kerkyacharian,G, Petrushev,P. and Picard,D.
    • Journal Title

      Constructive Approximation

      Volume: 47 Issue: 2 Pages: 277-320

    • DOI

      10.1007/s00365-018-9416-8

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Direct inverison formulas for the natural SFT2018

    • Author(s)
      OGAWA,Shigeyoshi
    • Journal Title

      Sankhya A

      Volume: 3 Issue: 2 Pages: 267-279

    • DOI

      10.1007/s13171-018-0128-8

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] BPE and a Noncausl Girsanov's Theorem2016

    • Author(s)
      Ogawa,S.
    • Journal Title

      Sankhya A

      Volume: 2 Issue: 2 Pages: 304-323

    • DOI

      10.1007/s13171-016-0087-x

    • Related Report
      2016 Research-status Report
    • Peer Reviewed
  • [Journal Article] A direct inversion formula for SFT2015

    • Author(s)
      Shigeyoshi Ogawa
    • Journal Title

      Sankhya A

      Volume: 77-1 Issue: 1 Pages: 30-45

    • DOI

      10.1007/s13171-014-0056-1

    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Journal Article] Identification of pseudo ito processes from its SFCs2014

    • Author(s)
      S.Ogawa & H.Uemura
    • Journal Title

      Bulletin des Sciences Mathematiques

      Volume: 138-1 Issue: 1 Pages: 147-163

    • DOI

      10.1016/j.bulsci.2013.12.003

    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Presentation] On the regularity of Gaussian processes indexed by Dirichlet spaces2018

    • Author(s)
      小川重義
    • Organizer
      日本数学会2018年度年会
    • Related Report
      2017 Annual Research Report
  • [Presentation] An essay on deterministic numerical solution of the SDE2018

    • Author(s)
      小川重義
    • Organizer
      Workshop「準乱数とその周辺」
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] 確率フーリエ変換の逆変換式について2017

    • Author(s)
      小川重義、植村英明
    • Organizer
      日本数学会2017年度年会
    • Place of Presentation
      首都大学東京(東京都八王子市)
    • Year and Date
      2017-03-24
    • Related Report
      2016 Research-status Report
  • [Presentation] On the direct inversion formulae for the natural SFT2017

    • Author(s)
      OGAWA,Shigeyoshi
    • Organizer
      Probability Seminar of National Taiwan Univ
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] 一般CONS の確率フーリエ係数による乱関数の復元について2017

    • Author(s)
      小川重義、植村英明
    • Organizer
      日本数学会秋季総合分科会
    • Related Report
      2017 Annual Research Report
  • [Presentation] On the direct inversion formulae for the natural SFT2016

    • Author(s)
      Ogawa, S.
    • Organizer
      Rencontres en Mathematiques a Paris-7
    • Place of Presentation
      LPMA, Universite de Paris-7 (France)
    • Year and Date
      2016-10-18
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] Some direct inversion formulae for the natural S2016

    • Author(s)
      Ogawa,S.
    • Organizer
      Probability Seminar of National Taiwan Univ.
    • Place of Presentation
      National Taiwan Univ. (Taipei)
    • Year and Date
      2016-05-16
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] BPE and a noncausal Giranov's theorem2016

    • Author(s)
      Ogawa, S.
    • Organizer
      Probability Seminar of National Taiwan Univ.
    • Place of Presentation
      National Taiwan Univ. (Taipei)
    • Year and Date
      2016-05-02
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] Formule directe d'inversion de la transforme de Fourier stochastiqu2015

    • Author(s)
      Ogawa,S
    • Organizer
      Seminaire de Proba et Finance a Paris-Est
    • Place of Presentation
      Univ Paris a Marne la Vallee(フランス)
    • Year and Date
      2015-11-26
    • Related Report
      2015 Research-status Report
    • Invited
  • [Presentation] Equation de particule brownienne et un Theoreme de Girsanov noncausal2015

    • Author(s)
      Ogawa,S
    • Organizer
      Seminaire de Probabilites de Paris-Nord
    • Place of Presentation
      Univ Paris-10(フランス)
    • Year and Date
      2015-11-25
    • Related Report
      2015 Research-status Report
    • Invited
  • [Presentation] On the inversion of stochastic Fourier transformation2015

    • Author(s)
      Ogawa,S
    • Organizer
      Seminar on Probability of Academia Sinica
    • Place of Presentation
      台湾大学数学研究所(台湾)
    • Year and Date
      2015-06-25
    • Related Report
      2015 Research-status Report
    • Invited
  • [Presentation] BPE and a noncausal counterpart of Girsanov's theorem2015

    • Author(s)
      小川重義
    • Organizer
      日本数学会春季総合分科会
    • Place of Presentation
      明治大学(東京都)
    • Year and Date
      2015-03-21
    • Related Report
      2014 Research-status Report
  • [Presentation] On the identification of noncausal functions from the SFCs2015

    • Author(s)
      小川重義、植村英明
    • Organizer
      日本数学会春季総合分科会
    • Place of Presentation
      明治大学(東京都)
    • Year and Date
      2015-03-21
    • Related Report
      2014 Research-status Report
  • [Presentation] 非因果的確率解析四方山話2015

    • Author(s)
      小川重義
    • Organizer
      確率論早春セミナー
    • Place of Presentation
      立命館大学草津キャンパス(滋賀県)
    • Year and Date
      2015-03-07
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] On the identification of pseudo Ito processes from the SFCs2014

    • Author(s)
      小川重義、植村英明
    • Organizer
      確率論シンポジウム
    • Place of Presentation
      京都大学数理解析研究所(京都府)
    • Year and Date
      2014-12-18
    • Related Report
      2014 Research-status Report
  • [Presentation] TFS et le probleme de l'inversion2014

    • Author(s)
      S.Ogawa
    • Organizer
      Seminaire Proba et Statist
    • Place of Presentation
      ENSTA (国立高等技術教員学校), Paris
    • Year and Date
      2014-12-15
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] A class of SPDEs called BPEs(1); transport phenomenon with infinite velocity2014

    • Author(s)
      S.Ogawa
    • Organizer
      Seminar on Probability and Statistics
    • Place of Presentation
      Math Inst of Academia Sinica in Taiwan
    • Year and Date
      2014-11-03
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] A class of SPDEs called BPEs(2); causality in stochastic mechanics2014

    • Author(s)
      S.Ogawa
    • Organizer
      Seminar on Probability and Statistics
    • Place of Presentation
      Math Inst of Academia Sinica in Taiwan
    • Year and Date
      2014-11-03
    • Related Report
      2014 Research-status Report
    • Invited
  • [Book] Noncausal Stochastic Calculus(単行本)2017

    • Author(s)
      OGAWA, Shigeyoshi (単著)
    • Total Pages
      2012
    • Publisher
      Springer
    • ISBN
      9784431565741
    • Related Report
      2017 Annual Research Report

URL: 

Published: 2014-04-04   Modified: 2019-03-29  

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