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Stochastic analysis for coagulation-fragmentation processes

Research Project

Project/Area Number 26400142
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

Handa Kenji  佐賀大学, 理工学部, 教授 (10238214)

Project Period (FY) 2014-04-01 – 2019-03-31
Project Status Completed (Fiscal Year 2018)
Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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凝結 / 分裂 / 相関関数 / 可逆分布 / 定常分布 / 点過程 / Poisson-Dirichlet分布 / 一意性 / split / merge / 区間分割
Outline of Final Research Achievements

The phenomena of coagulation and fragmentation are widely observed in nature. It is typical that the mathematical analysis for them is based on a nonlinear equation regarded as `the fundamental equation'. However, the previous studies are obliged to made the constraint on the growth order of the coagulation and fragmentation rates. In this research, introducing suitably a microscopic model describing random coagulation and fragmentation, and then taking a proper scaling limit, we have derived a certain class of coagulation-fragmentation equations with rates which are not necessarily satisfying the growth order previously required.

Academic Significance and Societal Importance of the Research Achievements

自然現象のみならず社会現象の記述・理解には数学は欠かせない.本研究での対象は,少なくとも歴史的には物理的背景を主な動機として持つが,数学的記述そのものは非常に汎用性が高いため,例えば生物等の社会的集団の合併・分割といった現象の研究においても,本研究で議論したモデル(微視的確率モデルおよび導出された非線形方程式で記述されるモデル)は一定の役割を担うことが可能となる場合があると期待される.

Report

(6 results)
  • 2018 Annual Research Report   Final Research Report ( PDF )
  • 2017 Research-status Report
  • 2016 Research-status Report
  • 2015 Research-status Report
  • 2014 Research-status Report
  • Research Products

    (8 results)

All 2018 2017 2015 2014

All Journal Article (1 results) Presentation (7 results) (of which Int'l Joint Research: 2 results,  Invited: 6 results)

  • [Journal Article] ランダムな凝結・分裂操作の双対性2018

    • Author(s)
      半田賢司
    • Journal Title

      統計数理研究所共同研究リポート

      Volume: 402 Pages: 43-54

    • Related Report
      2017 Research-status Report
  • [Presentation] Coagulation-fragmentation equations and underlying stochastic dynamics2018

    • Author(s)
      Kenji Handa
    • Organizer
      Second Interdisciplinary and Research Alumni Symposium iJaDe2018
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Coagulation-fragmentation equations and underlying stochastic dynamics2018

    • Author(s)
      Kenji Handa
    • Organizer
      Recent Progresses in Mathematical Theories for Biological Phenomena
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Random transpositions and coagulation-fragmentation equations2018

    • Author(s)
      半田賢司
    • Organizer
      関西確率論セミナー
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] ランダムな凝結・分裂操作の双対性2017

    • Author(s)
      半田賢司
    • Organizer
      無限分解可能過程に関連する諸問題
    • Related Report
      2017 Research-status Report
  • [Presentation] Hierarchical coagulation-fragmentation equations2017

    • Author(s)
      半田賢司
    • Organizer
      マルコフ過程とその周辺
    • Place of Presentation
      とくぎんトモニプラザ(徳島市)
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] Ewens分布を不変にする2つのMarkov連鎖2015

    • Author(s)
      半田賢司
    • Organizer
      研究集会「官庁統計データの公開における諸問題の研究と他分野への応用」
    • Place of Presentation
      統計数理研究所
    • Year and Date
      2015-12-11
    • Related Report
      2015 Research-status Report
    • Invited
  • [Presentation] Wright-Fisher拡散モデルの飛躍過程版とその定常分布2014

    • Author(s)
      半田賢司
    • Organizer
      数理生物モデルの現状と課題 No.2
    • Place of Presentation
      明治大学
    • Year and Date
      2014-05-18
    • Related Report
      2014 Research-status Report
    • Invited

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Published: 2014-04-04   Modified: 2020-03-30  

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