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Study of bi-generalized diffusion processes by means of limits of generalized diffusion processes

Research Project

Project/Area Number 25400139
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Basic analysis
Research InstitutionNara Women's University

Principal Investigator

Tomisaki Matsuyo  奈良女子大学, 名誉教授 (50093977)

Co-Investigator(Kenkyū-buntansha) TAKEMURA Tomoko  奈良女子大学, 研究院自然科学系, 助教 (40598140)
IIZUKA Masaru  九州歯科大学, 歯学部, 准教授 (20202830)
Project Period (FY) 2013-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2013: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Keywords広義拡散過程 / 双一般化拡散過程 / 極限定理 / 正値連続加法的汎関数 / 局所時間 / モランモデル / 強マルコフ性 / 斜積
Outline of Final Research Achievements

We considered properties of bi-generalized diffusion processes which are limits of generalized diffusion processes. We showed that weak mutation limits of the Moran model cannot be weak convergence limits in the space of cadlag functions, though they satisfy the strong Markov property. In the case that the limit of sequence of scale functions and that of speed measure functions have common discontinuous points, we showed that there exists a limit process whose state space has no topological structure. This result indicates that it is necessary to consider properties of bi-generalized diffusion processes by means of limit distributions instead of topological structure of state space.

Report

(4 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Research-status Report
  • 2013 Research-status Report
  • Research Products

    (16 results)

All 2016 2015 2014 Other

All Journal Article (6 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 6 results,  Open Access: 5 results,  Acknowledgement Compliant: 2 results) Presentation (9 results) (of which Int'l Joint Research: 1 results,  Invited: 8 results) Book (1 results)

  • [Journal Article] Exponent of inverse local time for harmonic transformed process2016

    • Author(s)
      Tomoko Takemura and Matsuyo Tomisaki
    • Journal Title

      Ann. Reports of Graduate School of Humanities and Sciences, Nara Women’s University

      Volume: 31 Pages: 127-138

    • NAID

      120006658042

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] A model of compensatory molecular evolution involving multiple sites in RNA molecules2016

    • Author(s)
      Junko Kusumi, Motoshi Ichinose, Masasuke Takefu, Robert Piskol, Wolfgang Stephan and Masaru Iizuka
    • Journal Title

      Journal of Theoretical Biology

      Volume: 388 Pages: 96-107

    • DOI

      10.1016/j.jtbi.2015.10.008

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Asymptotic behavior of Levy measure density corresponding to inverse local time2015

    • Author(s)
      Tomoko Takemura and Matsuyo Tomisaki
    • Journal Title

      Proceedigs of the Japan Academy

      Volume: 91 Issue: 1 Pages: 9-13

    • DOI

      10.3792/pjaa.91.9

    • NAID

      120006658129

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] The weak mutation and strong selection limit of the Moran model satisfies the strong Markov property2015

    • Author(s)
      Tomoko Takemura, Matsuyo Tomisaki and Masaru Iizuka
    • Journal Title

      Ann. Reports of Graduate School of Humanities and Sciences, Nara Women’s University

      Volume: 30 Pages: 105-112

    • NAID

      120006657952

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Intrinsic ultracontractivity and semismall perturbation for skew product diffusion operators2014

    • Author(s)
      Matsuyo Tomisaki
    • Journal Title

      Mathematisches Forschungsinstitut Oberwolfach, Dirichlet Form Theory and its Applications, Report

      Volume: 48 Issue: 4 Pages: 49-52

    • DOI

      10.4171/owr/2014/48

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] On the convergence of weak mutation limits of the Moran model in population genetics2014

    • Author(s)
      T. Takemura, M. Tomisaki and M. Iizuka
    • Journal Title

      Ann. Reports of Graduate School of Humanities and Sciences, Nara Women ’s University

      Volume: 29 Pages: 131-140

    • NAID

      110009863816

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Presentation] From diffusion processes to bi-generalized diffusion processes2015

    • Author(s)
      Matsuyo Tomisaki
    • Organizer
      Work shop on Dirichlet Forms and Stochastic Analysis 2015
    • Place of Presentation
      Technische Universitat Dresden, Germany
    • Year and Date
      2015-11-06
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Levy measure density corresponding to the inverse local time of harmonic transformed diffusion processes2014

    • Author(s)
      Matsuyo Tomisaki and Tomoko Takemura
    • Organizer
      関西大学確率論セミナー
    • Place of Presentation
      関西大学(吹田市)
    • Year and Date
      2014-12-04
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Levy measure density corresponding to the inverse local time of harmonic transformed diffusion processes2014

    • Author(s)
      Matsuyo Tomisaki and Tomoko Takemura
    • Organizer
      Work shop on Dirichlet Forms and Stochastic Analysis 2014
    • Place of Presentation
      ドレスデン工科大学(ドイツ)
    • Year and Date
      2014-10-27
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Intrinsic ultracontractivity and semismall perturbation for skew product diffusion operators2014

    • Author(s)
      Matsuyo Tomisaki
    • Organizer
      Oberwolfach Workshop, Dirichlet Form Theory and Its Applications
    • Place of Presentation
      オーベルヴォルファッハ数学研究所(ドイツ)
    • Year and Date
      2014-10-23
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Model of Compensatory Molecular Evolution with Direct and Indirect Compensation2014

    • Author(s)
      Masaru Iizuka
    • Organizer
      ミュンヘン大学バイオセンター・セミナー
    • Place of Presentation
      ミュンヘン大学(ドイツ・ミュンヘン市)
    • Year and Date
      2014-09-04
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Levy measure density corresponding to the inverse local time and the asymptotic behavior2014

    • Author(s)
      Tomoko Takemura and Matsuyo Tomisaki
    • Organizer
      International Congress of Mathematicians
    • Place of Presentation
      コエックス(韓国・ソウル市)
    • Year and Date
      2014-08-18
    • Related Report
      2014 Research-status Report
  • [Presentation] 集団遺伝学に現れる確率モデルの弱突然変異極限

    • Author(s)
      飯塚勝
    • Organizer
      九州確率論セミナー
    • Place of Presentation
      九州大学・伊都キャンパス(福岡県福岡市)
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Model of Compensatory Molecular Evolution with Indirect Compensation

    • Author(s)
      M. Iizuka
    • Organizer
      ミュンヘン大学バイオセンター
    • Place of Presentation
      ミュンヘン大学(ドイツ・ミュンヘン市)
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] h transform for Levy measure density

    • Author(s)
      T. Takemura and M.Tomisaki
    • Organizer
      Stochastic Processes and Mathematical Finance
    • Place of Presentation
      関西大学(大阪府吹田市)
    • Related Report
      2013 Research-status Report
    • Invited
  • [Book] Festschrift Masatoshi Fukushima (Editors Zhen-Qing Chen, Niels Jacob, Masayoshi Takeda, Toshihiro Uemura), Interdisciplinary Mathematical Sciences Vol.172015

    • Author(s)
      Sergio Albeverio, Martin Barlow, Krzysztof Burdzy, Nicolas Bouleau, Louis H Y Chen, Mu-Fa Chen, Xin Chen, Shizan Fang, Patrick J Fitzsimmons, Hans Follmer, Wolfhard Hansen, Masanori Hino, Hiroshi Kaneko, Witold Karwowski, Daehong Kim, Kazuhiro Kuwae, Panki Kim, Shinichi Kotani, Matsuyo Tomisaki 他
    • Total Pages
      607
    • Publisher
      World Scientific
    • Related Report
      2014 Research-status Report

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Published: 2014-07-25   Modified: 2019-07-29  

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