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

Multilateral research on infinite dimensional differential operators via stochastic analysis

Research Project

Project/Area Number 23740107
Research Category

Grant-in-Aid for Young Scientists (B)

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

Principal Investigator

KAWABI HIROSHI  岡山大学, 自然科学研究科, 准教授 (80432904)

Project Period (FY) 2011 – 2013
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2011: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Keywords確率解析 / 経路空間 / 微分作用素 / 一意性定理 / 確率偏微分方程式 / Rough Path理論 / 推移確率 / 漸近挙動 / Gibbs測度 / ラフパス解析
Research Abstract

I mainly studied uniqueness problems of differential operators and corresponding stochastic dynamics on infinite dimensional spaces via stochastic analysis. In particular, I proved strong uniqueness of Dirichlet operators for Gibbs measures which appear in quantum field theory and constructed a unique solution to the corresponding stochastic PDE by using Dirichlet form theory. Besides, I studied precise asymptotic behavior (i.e., the method of stationary phase) of some oscillatory functional integrals by combining Rough Path theory with Malliavin calculus. Motivated by this study of the stationary phase method, I also obtained an explicit effect of non-symmetry on the long time asymptotic behavior for a class of non-symmetric random walks on the triangular lattice.

Report

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

    (29 results)

All 2015 2014 2013 2012 2011 Other

All Journal Article (4 results) (of which Peer Reviewed: 4 results) Presentation (25 results) (of which Invited: 2 results)

  • [Journal Article] An explicit effect of non-symmetry of random walks on the triangular lattice2015

    • Author(s)
      S. Ishiwata, H. Kawabi and T. Teruya
    • Journal Title

      Math. J (Okayama Univ)

      Volume: Vol 57(To appear) Pages: 20-20

    • NAID

      120005525346

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] An explicit effect of non-symmetry of random walks on the triangular lattice2015

    • Author(s)
      Satoshi Ishiwata, Hiroshi Kawabi, Tsubasa Teruya
    • Journal Title

      Math. J. Okayama University

      Volume: 57

    • NAID

      120005525346

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Rockner, "Strong uniqueness for both Dirichlet operators and stochastic dynamics to Gibbs measures on a path space with exponential interactions"2012

    • Author(s)
      S. Albeverio, H. Kawabi and M
    • Journal Title

      J. Funct. Anal

      Volume: Vol 262 Pages: 602-638

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Strong uniqueness for both Dirichlet operators and stochastic dynamics to Gibbs measures on a path space with exponential interactions2012

    • Author(s)
      Sergio Albeverio, Hiroshi Kawabi and Michael Roeckner
    • Journal Title

      Journal of Functional Analysis

      Volume: 262

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Presentation] ある無限次元空間上の微分作用素の一意性問題とその周辺2014

    • Author(s)
      河備 浩司
    • Organizer
      RIMS 研究集会「確率解析」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2014-03-18
    • Related Report
      2013 Final Research Report
  • [Presentation] Stationary phase for rough differential equations2014

    • Author(s)
      Hiroshi Kawabi
    • Organizer
      Rough Paths : Theory and Applications, Institute for Pure and Applied Mathematics (IPAM)
    • Place of Presentation
      University of California at Los Angels (UCLA)
    • Year and Date
      2014-01-28
    • Related Report
      2013 Final Research Report
  • [Presentation] Uniqueness of Dirichlet forms related to stochastic quantization under exponential interaction in two-dimensional finite volume2013

    • Author(s)
      河備 浩司
    • Organizer
      科研費シンポジウム「マルコフ過程とその周辺」
    • Place of Presentation
      東北大学大学院理学研究科
    • Year and Date
      2013-11-15
    • Related Report
      2013 Final Research Report
  • [Presentation] Uniqueness of Dirichlet forms related to stochastic quantization under exponential interaction in two-dimensional finite volume2013

    • Author(s)
      Hiroshi Kawabi
    • Organizer
      German-Japanese Open Meeting on Stochastic Analysis
    • Place of Presentation
      Universitat Leipzig
    • Year and Date
      2013-09-09
    • Related Report
      2013 Final Research Report
  • [Presentation] An effect of non-symmetry on the transition probability of random walks on the triangular lattice2013

    • Author(s)
      河備 浩司
    • Organizer
      科研費シンポジウム「マルコフ過程とその周辺」
    • Place of Presentation
      京都大学大学院理学研究科
    • Year and Date
      2013-01-12
    • Related Report
      2013 Final Research Report
  • [Presentation] Strong uniqueness of diffusions to Gibbs measures on a path space with exponential and polynomial interactions2012

    • Author(s)
      Hiroshi Kawabi
    • Organizer
      Oberseminar Mathematik, Hausdorff Center for Mathematics
    • Place of Presentation
      Universitat Bonn
    • Year and Date
      2012-12-19
    • Related Report
      2013 Final Research Report
  • [Presentation] Strong uniqueness of diffusions to Gibbs measures on a path space with exponential and polynomial interactions2012

    • Author(s)
      Hiroshi Kawabi
    • Organizer
      Bielefeld Stochastic Afternoon, SFB701
    • Place of Presentation
      Faculty of Mathematics, Universitat Bielefeld
    • Year and Date
      2012-12-12
    • Related Report
      2013 Final Research Report
  • [Presentation] An effect of fragile non-symmetry on the transition probability of random walks on the triangular lattice2012

    • Author(s)
      石渡 聡, 河備 浩司, 照屋 翼
    • Organizer
      日本数学会秋期総合分科会
    • Place of Presentation
      九州大学
    • Year and Date
      2012-09-18
    • Related Report
      2013 Final Research Report
  • [Presentation] Strong uniqueness of diffusions on a path space with interactions2012

    • Author(s)
      河備 浩司
    • Organizer
      東北確率論セミナー
    • Place of Presentation
      東北大学大学院理学研究科
    • Year and Date
      2012-06-22
    • Related Report
      2013 Final Research Report 2012 Research-status Report
  • [Presentation] 三角格子上の非対称ランダムウォークの推移確率の長時間漸近挙動について2012

    • Author(s)
      河備 浩司
    • Organizer
      第31回小谷CREST 臨時セミナー
    • Place of Presentation
      東北大学大学院理学研究科
    • Year and Date
      2012-05-28
    • Related Report
      2013 Final Research Report
  • [Presentation] 三角格子上の非対称ランダムウォークの推移確率の長時間漸近挙動について2012

    • Author(s)
      河備 浩司
    • Organizer
      長岡高専数学談話会
    • Place of Presentation
      長岡工業高等専門学校
    • Year and Date
      2012-02-09
    • Related Report
      2013 Final Research Report 2011 Research-status Report
  • [Presentation] 三角格子上の非対称ランダムウォークの推移確率の長時間漸近挙動について2012

    • Author(s)
      石渡 聡, 河備 浩司, 照屋 翼
    • Organizer
      日本数学会中国・四国支部例会
    • Place of Presentation
      岡山大学環境理工学部
    • Year and Date
      2012-01-22
    • Related Report
      2013 Final Research Report 2011 Research-status Report
  • [Presentation] Strong uniqueness of diffusions to Gibbs measures on a path space with exponential interactions2012

    • Author(s)
      河備 浩司
    • Organizer
      九州確率論セミナー
    • Place of Presentation
      九州大学大学院数理学研究院
    • Year and Date
      2012-01-06
    • Related Report
      2013 Final Research Report 2011 Research-status Report
  • [Presentation] Strong uniqueness of diffusions to Gibbs measures on a path space with exponential interactions2011

    • Author(s)
      Hiroshi Kawabi
    • Organizer
      Invited Session : Stochastic Partial Differential Equations, 5th International Conference on Stochastic Analysis and its Applications
    • Place of Presentation
      Hausdorff Center for Mathematics Universitat Bonn
    • Year and Date
      2011-09-05
    • Related Report
      2013 Final Research Report
  • [Presentation] Precise asymptotics of functional integrals for infinite dimensional Ito-Lyons map of Brownian rough paths2011

    • Author(s)
      Hiroshi Kawabi
    • Organizer
      Invited Session : Rough Path Analysis, The 35th Conference on Stochastic Processes and their Applications (SPA)
    • Place of Presentation
      Oaxaca
    • Year and Date
      2011-06-24
    • Related Report
      2013 Final Research Report
  • [Presentation] Strong uniqueness of diffusions to Gibbs measures on a path space with exponential interactions2011

    • Author(s)
      Hiroshi Kawabi
    • Organizer
      Stochastic Partial Differential Equations and Related Topics(招待講演)
    • Place of Presentation
      Chern Institute of Mathematics, Nankai University, 中国
    • Related Report
      2011 Research-status Report
  • [Presentation] Precise asymptotics of functional integrals for infinite dimensional Ito-Lyons map of Brownian rough paths2011

    • Author(s)
      Hiroshi Kawabi
    • Organizer
      35th Conference on Stochastic Processes and their Applications (SPA)(招待講演)
    • Place of Presentation
      Oaxaca, メキシコ
    • Related Report
      2011 Research-status Report
  • [Presentation] Strong uniqueness of diffusions to Gibbs measures on a path space with exponential interactions2011

    • Author(s)
      Hiroshi Kawabi
    • Organizer
      5th International Conference on Stochastic Analysis and its Applications(招待講演)
    • Place of Presentation
      Hausdorff Center for Mathematics, University of Bonn, ドイツ
    • Related Report
      2011 Research-status Report
  • [Presentation] Uniqueness of Dirichlet forms related to stochastic quantization under exponential interaction in two-dimensional finite volume

    • Author(s)
      Hiroshi Kawabi
    • Organizer
      German-Japanese Open Meeting on Stochastic Analysis
    • Place of Presentation
      University of Leipzig
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Uniqueness of Dirichlet forms related to stochastic quantization under exponential interaction in two-dimensional finite volume

    • Author(s)
      河備 浩司
    • Organizer
      マルコフ過程とその周辺
    • Place of Presentation
      東北大学大学院理学研究科
    • Related Report
      2013 Annual Research Report
  • [Presentation] Stationary phase for rough differential equations

    • Author(s)
      Hiroshi Kawabi
    • Organizer
      Rough Paths: Theory and Applications
    • Place of Presentation
      IPAM, UCLA
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] 三角格子上の非対称ランダムウォークの推移確率の長時間漸近挙動について

    • Author(s)
      河備 浩司
    • Organizer
      第31回臨時小谷CRESTセミナー
    • Place of Presentation
      東北大学大学院理学研究科
    • Related Report
      2012 Research-status Report
  • [Presentation] An effect of fragile non-symmetry on the transition probability of random walks on the triangular lattice

    • Author(s)
      石渡 聡、河備 浩司、照屋 翼
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      九州大学
    • Related Report
      2012 Research-status Report
  • [Presentation] Strong uniqueness of diffusions to Gibbs measures on a path space with exponential and polynomial interactions

    • Author(s)
      Hiroshi Kawabi
    • Organizer
      Bielefeld Stochastic Afternoon
    • Place of Presentation
      University of Bielefeld、ドイツ
    • Related Report
      2012 Research-status Report
  • [Presentation] Strong uniqueness of diffusions to Gibbs measures on a path space with exponential and polynomial interactions

    • Author(s)
      Hiroshi Kawabi
    • Organizer
      Oberseminar Mathematik
    • Place of Presentation
      University of Bonn、ドイツ
    • 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