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Extensions of reflecting Markov processes on unbounded domains

Research Project

Project/Area Number 22540125
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionOsaka University

Principal Investigator

FUKUSHIMA Masatoshi  大阪大学, その他部局等, 名誉教授 (90015503)

Project Period (FY) 2010 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2012: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Keywords無限錐 / 反射壁ブラウン運動 / 多重連結領域 / 小松・レブナー微分方程式 / かがりブラウン運動 / SKLE / 1次元極小拡散過程 / 対称性 / 対称拡散拡張 / 2次元かがりブラウン運動 / 小松レブナー方程式 / ランダム曲線 / SLE / 等角不変 / 確率微分方程式 / 3次元反射壁ブラウン運動 / 2次元縢りブラウン運動 / 小松-Loewner微分方程式 / 等角写像 / 1次元拡散過程 / 一般境界条件 / 無限錘 / 対称マルコフ的拡張 / 非対称安定型過程 / 非対称ディリクレ形式 / 小松-Leowner方程式
Research Abstract

1. The time changed reflecting Brownian motion on a 3-space consisting of two infinite cones is shown to admit 4 and only 4 possible symmetric Markovian extensions.
2. The Komatu-Loewner differential equation for a multiply connected planar domain is derived by the Brownian motion with darning (BMD). The notion of stochastic Loewner evolution (SLE) for simply connected domains is extended to multiply connected domains as stochastic Komatu-Loewner evolution (SKLE).
3. The minimal diffusion on an interval is shown to be symmetric for the canonical measure and all its symmetric diffusion extensions are identified in relation to Ito-McKean’ s theory. As a result, the one-dimensional diffusions with general boundary conditions can be directly constructed by means of regular Dirichlet forms.

Report

(4 results)
  • 2012 Annual Research Report   Final Research Report ( PDF )
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (19 results)

All 2013 2012 2011 2010 Other

All Journal Article (9 results) (of which Peer Reviewed: 9 results) Presentation (6 results) Book (4 results)

  • [Journal Article] On general boundary conditions for one-dimensional diffusions with symmetry2013

    • Author(s)
      M. Fukushima
    • Journal Title

      Journal of Mathematical Society of Japan

    • NAID

      130003394358

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] A localization formula in Dirichlet form theory2012

    • Author(s)
      Z.-Q. Chen, M. Fukushima
    • Journal Title

      Proceedings of the AmericanMathematical Society

      Volume: 140 Pages: 1815-1822

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Jump-type Hunt processes generated by lower bounded semi-Dirichlet forms2012

    • Author(s)
      M. Fukushima, T. Uemura
    • Journal Title

      The Annals of Probability

      Volume: 40 Pages: 858-889

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] A localization formula in Dirichlet form theory2012

    • Author(s)
      Z.-Q. Chen, M. Fukushima
    • Journal Title

      Proceedings of American Mathematical Society

      Volume: 140 Pages: 1815-1822

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Jump-type Hunt processes generated by lower bounded semi-Dirichlet forms2012

    • Author(s)
      M. Fukushima, and T. Uemura
    • Journal Title

      Ann. Probab.

      Volume: 40 Issue: 2 Pages: 858-889

    • DOI

      10.1214/10-aop633

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Jump tyye Hunt processes generated by lower bounded semi-Dirichlet forms2012

    • Author(s)
      M.Fukushima, T.Uemura
    • Journal Title

      Annals of Probability

      Volume: (In Press)

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A localization formula in Dirichlet form theory2012

    • Author(s)
      Z.-Q.Chen, M.Fukushima
    • Journal Title

      Proceedings of American Mathematical Society

      Volume: (In Press)

    • Related Report
      2011 Annual Research Report 2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Jump-type Hunt processes generated by lower bounded semi-Dirichlet forms2011

    • Author(s)
      M.Fukushima, T.Uemura
    • Journal Title

      Annales of Probability

      Volume: (In Press)

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] From one dimensional diffusions to symmetric Markov processes2010

    • Author(s)
      M. Fukushima
    • Journal Title

      Stochastic Processes and their Applications

      Volume: 120 Pages: 590-604

    • Related Report
      2012 Final Research Report 2010 Annual Research Report
    • Peer Reviewed
  • [Presentation] Brownian motion with darning applied to KL and BF equations for planar slit domains,Stochastic Analysis and Applications2012

    • Author(s)
      福島 正俊
    • Organizer
      German-Japanese bilateral project
    • Place of Presentation
      岡山大学
    • Year and Date
      2012-09-26
    • Related Report
      2012 Final Research Report
  • [Presentation] On Brownian motion with darning and Komatu-Loewner equation for multiply connected planar domains2011

    • Author(s)
      福島 正俊
    • Organizer
      Foundation of Stochastic Analysis
    • Place of Presentation
      Banff, Canada
    • Year and Date
      2011-09-20
    • Related Report
      2012 Final Research Report
  • [Presentation] On Brownian motion with darning and Komatu-Loewner equation for multiply connected planar domains2011

    • Author(s)
      Masatoshi Fukushima
    • Organizer
      Foundation of Stochastic Analysis
    • Place of Presentation
      Banff, Canada(招待講演)
    • Year and Date
      2011-09-20
    • Related Report
      2011 Annual Research Report
  • [Presentation] Jump-type Hunt processesgenerated by lower bounded semi-Dirichlet forms2010

    • Author(s)
      福島 正俊
    • Organizer
      4-th International Conference on Stochastic Analysis and Its Applications
    • Place of Presentation
      関西大学
    • Year and Date
      2010-08-30
    • Related Report
      2012 Final Research Report
  • [Presentation] Jump-type Hunt processes generated by lower bounded semi-Dirichlet forms2010

    • Author(s)
      M.Fukushima
    • Organizer
      4^<th> International Conference on Stochastic Analysis and Its Applications
    • Place of Presentation
      関西大学
    • Year and Date
      2010-08-30
    • Related Report
      2010 Annual Research Report
  • [Presentation] Brownian motion with darning applied to KL and BF equations for planar slit domains

    • Author(s)
      M. Fukushima
    • Organizer
      Stochastic Analysis and Applications, German-Japanese bilateral research project
    • Place of Presentation
      岡山大学
    • Related Report
      2012 Annual Research Report
  • [Book] Symmetric Markov Processes, Time Change, and Boundary Theory2012

    • Author(s)
      Z.-Q. Chen, M. Fukushima
    • Publisher
      Princeton University Press
    • Related Report
      2012 Annual Research Report 2012 Final Research Report
  • [Book] Symmetric Markov Processes, Time Change, and Boundary Theory2012

    • Author(s)
      Z.-Q.Chen, M.Fukushima
    • Total Pages
      479
    • Publisher
      Princeton University Press
    • Related Report
      2011 Annual Research Report
  • [Book] Dirichlet Forms and Symmetric Markov Processes, 2-ndrevised and extended edition2010

    • Author(s)
      M. Fukushima, Y. Oshima, M. Takeda
    • Publisher
      De Gruyter
    • Related Report
      2012 Final Research Report
  • [Book] Dirichlet Forms and Symmetric Markov Processes, 2^<nd> revised and extended edition2010

    • Author(s)
      M.Fukushima, Y.Oshima, M.Takeda (共著)
    • Publisher
      De Gruyter
    • Related Report
      2010 Annual Research Report

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Published: 2010-08-23   Modified: 2019-07-29  

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