Research about effects of boundary states on conditional distributions

• Project/Area Number: 19540129
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Nara Women's University
• Principal Investigator: TOMISAKI Matsuyo Nara Women's University, 理学部, 教授 (50093977)
• Co-Investigator(Kenkyū-buntansha): SHINODA Masato 奈良女子大学, 理学部, 准教授 (50271044) ; IIZUKA Masaru 九州歯科大学, 歯学部, 准教授 (20202830)
• Project Period (FY): 2007 – 2009
• Project Status: Completed (Fiscal Year 2009)
• Budget Amount: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000); Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2008: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2007: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
• Keywords: 広義拡散過程 / 広義拡散作用素 / 境界条件 / 調和変換 / マルコフ性

Research Abstract

The method of harmonic transform is a useful one to analyze some properties of Green kernels and diffusion processes. It should be noted that these Green kernels and diffusion processes are minimal. However minimal stochastic processes are not always treated in applied mathematics such as population genetics. In our research, conditional distributions of non minimal generalized diffusion processes and the effect of asymptotic behavior of sample paths near the boundaries on conditional distributions are investigated.

Research Products

• [Journal Article] Transition probability densities of birth and death processes with finite state space (2010)
  • Author(s): Masaru Iizuka, Matsuyo Tomisaki
  • Journal Title: Annual Reports of Graduate School of Humanities and Sciences Vol.25 Pages: 271-284
  • NAID: 110008668276
• [Journal Article] Feller property of skew product diffusion processes (2010)
  • Author(s): T.Takemura, M.Tomisaki
  • Journal Title: Osaka Journal of Mathematics
  • NAID: 120006581110
  • Peer Reviewed
• [Journal Article] Transition probability densities of birth and death processes with finite state space (2009)
  • Author(s): M.Iizuka, M.Tomisaki
  • Journal Title: Ann.Reports of Graduate School of Humanities and Sciences, Nara Women's University 25 Pages: 271-284
  • NAID: 110008668276
  • Peer Reviewed
• [Journal Article] Winning strategy of the memory game (2008)
  • Author(s): Masato Shinoda
  • Journal Title: IPSJ Symposium Series Pages: 181-188
  • NAID: 170000080358
  • Peer Reviewed
• [Journal Article] Compensatory evolution in diploid population (2008)
  • Author(s): Motoshi Ichinose, Masaru Iizuka, Tomoyuki Kado, Masasuke Takefu
  • Journal Title: Theoretical Population Biology Vol.74 Pages: 199-207
  • Peer Reviewed
• [Journal Article] Compensatory evolution in diploid populations (2008)
  • Author(s): M. Ichinose
  • Journal Title: Theoretical Population Biology 74 Pages: 199-207
  • Peer Reviewed
• [Journal Article] Winning strategy of the memory game (2008)
  • Author(s): M. Shinoda
  • Journal Title: IPSJ Sympos ium Series 2008 Pages: 181-188
  • NAID: 170000080358
  • Peer Reviewed
• [Journal Article] Conditional distributions which do not satisfy the Chapman-Kolmogorov equation (2007)
  • Author(s): Masaru Iizuka, Miyuki Maeno, Matsuyo Tomisaki
  • Journal Title: Journal of the Mathematical Society of Japan Vol.59 Pages: 971-983
  • NAID: 10019989225
  • Peer Reviewed
• [Journal Article] Intrinsic ultracontractivity and small perturbation for one dimensional generalized diffusion operators (2007)
  • Author(s): Matsuyo Tomisaki
  • Journal Title: Journal of Functional Analysis Vol.251 Pages: 289-324
• [Journal Article] Intrinsic ultracontractivity and small perturbation for one dimensional generalized diffusion operators (2007)
  • Author(s): M. Tomisaki
  • Journal Title: Journal of Functional Analysis 251 Pages: 289-324
  • Peer Reviewed
• [Journal Article] Conditional distributions which do not satisfy the Chapman-Kolmogorov equation (2007)
  • Author(s): M. Iizuka
  • Journal Title: Journal of the Mathematical Society of Japan 59 Pages: 971-983
  • NAID: 10019989225
  • Peer Reviewed
• [Journal Article] Feller property of skew product diffusion processes
  • Author(s): Tomoko Takemura, Matsuyo Tomisaki
  • Journal Title: Osaka Journal of Mathematics (掲載決定)
  • NAID: 120006581110
  • Peer Reviewed
• [Presentation] タンパク質共進化機構の集団遺伝学的考察 (2009)
  • Author(s): 飯塚勝
  • Organizer: 日本生物物理学会第47回年会
  • Place of Presentation: 徳島文理大学(徳島県)
  • Year and Date: 2009-10-30
• [Presentation] Uniform spanning trees and loop-erased random walks on the pre-Sierpinski gasket (2009)
  • Author(s): 篠田正人
  • Organizer: 日本数学会
  • Place of Presentation: 大阪大学(大阪府)
  • Year and Date: 2009-09-24
• [Presentation] h変換された一次元広義拡散過程の大域的性質 (2009)
  • Author(s): 嶽村智子, 富崎松代
  • Organizer: 日本数学会
  • Place of Presentation: 東京大学(東京都)
  • Year and Date: 2009-03-26
• [Presentation] Winning strategy of the memory game (2008)
  • Author(s): 篠田正人
  • Organizer: ゲームプログラミングワークショップ
  • Place of Presentation: 箱根セミナーハウス(神奈川県)
  • Year and Date: 2008-11-09
• [Presentation] Winning strategy of the memory game (2008)
  • Author(s): 篠田正人
  • Organizer: ゲームプログラミングワークショップ2008
  • Place of Presentation: 箱根セミナーハウス
  • Year and Date: 2008-11-09
• [Presentation] 直積グラフにおけるパーコレーション無限クラスターの個数について (2008)
  • Author(s): 篠田正人
  • Organizer: 研究集会「大規模作用系の確率解析」
  • Place of Presentation: 東京大学(東京都)
  • Year and Date: 2008-11-04
• [Presentation] 直積グラフにおけるパーコレーション無限クラスターの個数について (2008)
  • Author(s): 篠田正人
  • Organizer: 研究集会「大規模作用系の確率解析」
  • Place of Presentation: 東京大学
  • Year and Date: 2008-11-04
• [Presentation] Models of Compensatory Molecular Evolution (2008)
  • Author(s): Masaru Iizuka, Motoshi Ichinose, Tomoyuki Kado, Masasuke Takefu
  • Organizer: The XXth International Congress of Genetics
  • Place of Presentation: International Congress Centrum (Berlin)
  • Year and Date: 2008-07-14
• [Presentation] Models of compensatory molecular evolution (2008)
  • Author(s): M. Iizuka
  • Organizer: 第20回国際遺伝学会議(The XXth International Congress of Genetics at Berlin)
  • Place of Presentation: International Congress Centrum, Berlin(ドイツ)
  • Year and Date: 2008-07-14
• [Presentation] The number of infinite percolation clusters on some graph products (2007)
  • Author(s): 篠田正人
  • Organizer: Stochastic Analysis on Large Scale Interacting Systems
  • Place of Presentation: 九州大学西新プラザ(福岡県)
  • Year and Date: 2007-10-25
• [Presentation] The number of infinite percolation clusters on some graph products (2007)
  • Author(s): 篠田正人
  • Organizer: Stochastic Analysis on Large Scale Interacting Systems
  • Place of Presentation: 九州大学西新プラザ
  • Year and Date: 2007-10-25
• [Presentation] ある種の直積グラフにおけるパーコレーション無限クラスターの個数について (2007)
  • Author(s): 篠田正人
  • Organizer: 統計力学神戸セミナー
  • Place of Presentation: 神戸大学
  • Year and Date: 2007-05-08
• [Presentation] マルコフ過程入門 (2007)
  • Author(s): 飯塚 勝
  • Organizer: 九州大学六本松地区・集団遺伝学セミナー
  • Place of Presentation: 九州大学
  • Year and Date: 2007-05-07