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Non regular limits of one-dimensional generalized diffusion processes

Research Project

Project/Area Number 22540132
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 InstitutionNara Women's University

Principal Investigator

TOMISAKI Matsuyo  奈良女子大学, 副学長 (50093977)

Co-Investigator(Kenkyū-buntansha) IIZUKA Masaru  九州歯科大学, 歯学部, 准教授 (20202830)
MORITOH Yumi  奈良女子大学, 理学部, 特任助教 (80611128)
Project Period (FY) 2010 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords広義拡散過程 / 双一般化拡散過程 / 出生死滅過程 / モラン・モデル / 調和変換 / レヴィ測度 / モランモデル / 条件付き確率過程 / マルコフ性
Research Abstract

We considered the phenomena where we have non regular limits of one-dimensional generalized diffusion processes. When the limit of scale functions and that of speed measure functions have common discontinuous points, we proved the convergence of transition probabilities and showed that the limit process can be a one-dimensional bi-generalized diffusion process, by means of convergence of Green functions. We also investigated the effect of boundary conditions on harmonic transform of one-dimensional generalized diffusion processes. Further we showed some limit theorems for Moran model in population genetics.

Report

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

    (32 results)

All 2013 2012 2011 2010 Other

All Journal Article (8 results) (of which Peer Reviewed: 8 results) Presentation (24 results) (of which Invited: 3 results)

  • [Journal Article] Weak mutation limits of the Moran model in population genetics, Ann. Reports of Graduate School of Humanities and Sciences2013

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

      Nara Women's University

      Volume: vol.28 Pages: 1-12

    • URL

      http://hdl.handle.net/10935/3338

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Weak mutation limits of the Moran model in population genetics2013

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

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

      Volume: 28 Pages: 1-12

    • NAID

      40019727003

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] <i>h</i> TRANSFORM OF ONE-DIMENSIONAL GENERALIZED DIFFUSION OPERATORS2012

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

      Kyushu Journal of Mathematics

      Volume: 66 Issue: 1 Pages: 171-191

    • DOI

      10.2206/kyushujm.66.171

    • NAID

      130002543068

    • ISSN
      1340-6116, 1883-2032
    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] h transform of one-dimensional generalized diffusion operators2012

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

      Kyushu Journal of Mathematics

      Volume: 66 Pages: 171-191

    • NAID

      130002543068

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Recurrence/transience criteria for skew product diffusion processes2011

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

      Proceedigs of the Japan Academy

      Volume: Vol.87, Ser. A, no.7 Issue: 7 Pages: 119-122

    • DOI

      10.3792/pjaa.87.119

    • NAID

      120006657512

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Recurrence/transience criteria for skew product diffusion processes2011

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

      Proceedings of the Japan Academy, Ser.A

      Volume: 87 Pages: 119-122

    • NAID

      120006657512

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Conditional processes induced by birth and death processes2010

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

      International Journal of Mathematics and Mathematical Sciences

      Volume: Volume 2010, Article ID 784567 Issue: 1 Pages: 24-24

    • DOI

      10.1155/2010/784567

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Conditional Processes Induced by Birth and Death Processes2010

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

      International Journal of Mathematics and Mathematical Sciences

      Volume: 2010 Pages: 1-24

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Presentation] Intrinsic ultracontractivity and semismall perturbations for skew product diffusion operators2013

    • Author(s)
      M. Tomisaki
    • Organizer
      Recent topics on Markov processes
    • Place of Presentation
      奈良女子大学(奈良)
    • Year and Date
      2013-02-10
    • Related Report
      2012 Final Research Report
  • [Presentation] 集団遺伝学に現れる確率モデルの弱突然変異極限2013

    • Author(s)
      M.Iizuka
    • Organizer
      Recenttopicson Markovprocesses
    • Place of Presentation
      奈良女子大学(奈良)
    • Year and Date
      2013-02-10
    • Related Report
      2012 Final Research Report
  • [Presentation] Levy measure density corresponding to inverse local time2012

    • Author(s)
      T.Takemura and M.Tomisaki
    • Organizer
      Stochastic Analysis and Applications German-Japanese bilateral research project
    • Place of Presentation
      岡山大学(岡山)
    • Year and Date
      2012-09-27
    • Related Report
      2012 Final Research Report
  • [Presentation] Levy measure density corresponding to inverse local time2012

    • Author(s)
      T.Takemura and M.Tomisaki
    • Organizer
      日本数学会 2012年度秋季総合分科会
    • Place of Presentation
      九州大学(福岡)
    • Year and Date
      2012-09-18
    • Related Report
      2012 Final Research Report
  • [Presentation] The effects of back mutation on compensatory molecular evolution2012

    • Author(s)
      M.Iizuka
    • Place of Presentation
      ミュンヘン大学バイオセンター(ドイツ)
    • Year and Date
      2012-09-12
    • Related Report
      2012 Final Research Report
  • [Presentation] Levy measure density corresponding to inverse local time2012

    • Author(s)
      T.Takemura and M.Tomisaki
    • Organizer
      6th International Conference on Stochastic Analysis and Its Applications
    • Place of Presentation
      Conference Center in Bedlewo (ポーランド)
    • Year and Date
      2012-09-11
    • Related Report
      2012 Final Research Report
  • [Presentation] Minkowskiの定理の一般化(1950,H.P.Mulholland)に関する話題2012

    • Author(s)
      Y.Moritoh
    • Organizer
      Ideas and Methods of Harmonic Analysis
    • Place of Presentation
      奈良女子大学(奈良)
    • Year and Date
      2012-06-20
    • Related Report
      2012 Final Research Report
  • [Presentation] 一次元拡散過程の非正則な拡散過程への収束について2012

    • Author(s)
      M.Tomisaki
    • Organizer
      非正則な拡散過程における諸問題
    • Place of Presentation
      奈良女子大学(奈良)
    • Year and Date
      2012-01-29
    • Related Report
      2012 Final Research Report
  • [Presentation] 一次元広義拡散過程のh変換2011

    • Author(s)
      T.Takemura and M.Tomisaki
    • Organizer
      日本数学会2011年度秋季総合分科会
    • Place of Presentation
      信州大学(松本)
    • Year and Date
      2011-09-28
    • Related Report
      2012 Final Research Report 2011 Annual Research Report
  • [Presentation] Conditional processes induced by one-dimensional generalized diffusion processes related to stochastic models in population genetics2011

    • Author(s)
      M.Iizuka
    • Organizer
      5th International Conference on Stochastic Analysis and its Applications
    • Place of Presentation
      ボン大学(ドイツ)
    • Year and Date
      2011-09-09
    • Related Report
      2012 Final Research Report
  • [Presentation] Conditional processes induced by one-dimensional generalized diffusion processes related to stochastic models in population genetics2011

    • Author(s)
      Masaru Iizuka
    • Organizer
      5th International Conference on Stochastic Analysis and its Applications
    • Place of Presentation
      ボン大学(ドイツ)(招待講演)
    • Year and Date
      2011-09-09
    • Related Report
      2011 Annual Research Report
  • [Presentation] Recurrence/transience criteria for skew product diffusions2011

    • Author(s)
      T.Takemura and M.Tomisaki
    • Organizer
      5th International Conference on Stochastic Analysis and its Applications
    • Place of Presentation
      ボン大学(ドイツ)
    • Year and Date
      2011-09-08
    • Related Report
      2012 Final Research Report
  • [Presentation] Eecurrence/Transience criteria for skew product diffusions2011

    • Author(s)
      T.Takemura, M.Tomisaki
    • Organizer
      5th International Conference on Stochastic Analysis and its Applications
    • Place of Presentation
      ボン大学(ドイツ)(招待講演)
    • Year and Date
      2011-09-08
    • Related Report
      2011 Annual Research Report
  • [Presentation] Models of compensatory molecular Evolution2011

    • Author(s)
      M.Iizuka
    • Organizer
      Annual Conference of Society for Molecular Biology and Evolution
    • Place of Presentation
      京都大学(京都)
    • Year and Date
      2011-07-27
    • Related Report
      2012 Final Research Report
  • [Presentation] Models of compensatory molecular evolution2011

    • Author(s)
      Masaru Iizuka
    • Organizer
      Annual Conference of Society for Molecular Biology and Evolution
    • Place of Presentation
      京都大学(京都)(招待講演)
    • Year and Date
      2011-07-27
    • Related Report
      2011 Annual Research Report
  • [Presentation] h transform of one dimensional generalized diffusion operators2010

    • Author(s)
      M.Tomisaki
    • Organizer
      4th International Conference on Stochastic Analysis and its Applications
    • Place of Presentation
      関西大学(大阪)
    • Year and Date
      2010-08-31
    • Related Report
      2012 Final Research Report
  • [Presentation] h-transform of one dimensional generalized diffusion operators2010

    • Author(s)
      M.Tomisaki
    • Organizer
      4th International Conference on Stochastic Analysis and Its Applications
    • Place of Presentation
      Kansai University, Suita, Osaka, Japan
    • Year and Date
      2010-08-31
    • Related Report
      2010 Annual Research Report
  • [Presentation] Intrinsic ultracontractivity and semismall perturbations for skew product diffusion operators

    • Author(s)
      M. Tomisaki
    • Organizer
      Recent topics on Markov processes
    • Place of Presentation
      奈良女子大学(奈良)
    • Related Report
      2012 Annual Research Report
    • Invited
  • [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)
      M. Iizuka
    • Organizer
      Recent topics on Markov processes
    • Place of Presentation
      奈良女子大学(奈良)
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Levy measure density corresponding to inverse local time

    • Author(s)
      T. Takemura and M. Tomisaki
    • Organizer
      "Stochastic Analysis and Applications" German-Japanese bilateral research project
    • Place of Presentation
      岡山大学(岡山)
    • Related Report
      2012 Annual Research Report
  • [Presentation] Levy measure density corresponding to inverse local time

    • Author(s)
      T. Takemura and M. Tomisaki
    • Organizer
      日本数学会 2012年度秋季総合分科会
    • Place of Presentation
      九州大学(福岡)
    • Related Report
      2012 Annual Research Report
  • [Presentation] The effects of back mutation on compensatory molecular evolution

    • Author(s)
      M. Iizuka
    • Organizer
      Biocenter, Univ. of Munich, Germany
    • Place of Presentation
      ミュンヘン大学バイオセンター(ドイツ)
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Levy measure density corresponding to inverse local time

    • Author(s)
      T. Takemura and M. Tomisaki
    • Organizer
      6th International Conference on Stochastic Analysis and Its Applications
    • Place of Presentation
      Conference Center in Bedlewo (ポーランド)
    • Related Report
      2012 Annual Research Report
  • [Presentation] Minkowski の定理の一般化(1950, H. P. Mulholland) に関する話題

    • Author(s)
      Y. Moritoh
    • Organizer
      Ideas and Methods of Harmonic Analysis, Nara (3)
    • Place of Presentation
      奈良女子大学(奈良)
    • Related Report
      2012 Annual Research Report

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

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