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

• Project/Area Number: 25400139
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Nara 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: ¥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.

Research Products

• [Journal Article] Exponent of inverse local time for harmonic transformed process (2016)
  • 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
  • Peer Reviewed / Open Access
• [Journal Article] A model of compensatory molecular evolution involving multiple sites in RNA molecules (2016)
  • 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
  • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Asymptotic behavior of Levy measure density corresponding to inverse local time (2015)
  • 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
  • Peer Reviewed / Open Access
• [Journal Article] The weak mutation and strong selection limit of the Moran model satisfies the strong Markov property (2015)
  • 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
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Intrinsic ultracontractivity and semismall perturbation for skew product diffusion operators (2014)
  • 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
  • Peer Reviewed / Open Access
• [Journal Article] On the convergence of weak mutation limits of the Moran model in population genetics (2014)
  • 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
  • Peer Reviewed
• [Presentation] From diffusion processes to bi-generalized diffusion processes (2015)
  • 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
  • Int'l Joint Research / Invited
• [Presentation] Levy measure density corresponding to the inverse local time of harmonic transformed diffusion processes (2014)
  • 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
  • Invited
• [Presentation] Levy measure density corresponding to the inverse local time of harmonic transformed diffusion processes (2014)
  • Author(s): Matsuyo Tomisaki and Tomoko Takemura
  • Organizer: Work shop on Dirichlet Forms and Stochastic Analysis 2014
  • Place of Presentation: ﾄﾞﾚｽﾃﾞﾝ工科大学（ドイツ）
  • Year and Date: 2014-10-27
  • Invited
• [Presentation] Intrinsic ultracontractivity and semismall perturbation for skew product diffusion operators (2014)
  • 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
  • Invited
• [Presentation] Model of Compensatory Molecular Evolution with Direct and Indirect Compensation (2014)
  • 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
  • Invited
• [Presentation] Levy measure density corresponding to the inverse local time and the asymptotic behavior (2014)
  • 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
• [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）
  • 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）
  • 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）
  • Invited
• [Book] Festschrift Masatoshi Fukushima (Editors Zhen-Qing Chen, Niels Jacob, Masayoshi Takeda, Toshihiro Uemura), Interdisciplinary Mathematical Sciences Vol.17 (2015)
  • 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