Stationary distribution and limit distribution of reflecting stochastic process and its biological applications

• Project/Area Number: 21540131
• 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: Hiroshima University
• Principal Investigator: SAISHO Yasumasa 広島大学, 大学院・工学研究院, 准教授 (70195973)
• Co-Investigator(Kenkyū-buntansha): KANAGAWA Shuya 東京都市大学, 知識工学部, 教授 (50185899) ; HATAUE Itaru 金沢大学, 理工学域電子情報学系, 教授 (50218476)
• Project Period (FY): 2009 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000); Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2009: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
• Keywords: 確率論 / 反射壁確率過程 / 極限分布 / 数理モデル / 数理生物学 / 定常分布 / セミの生態 / DNAの損傷 / 2本鎖切断

Research Abstract

Concrete examples of non-trivial 1-dimensional reflecting process having limit distribution and stationary distribution were showed. For biological applications, we constructed a stochastic model and consider whether this sexual difference of eclosion periods works against mating or not. We also calculated the dose dependence of dsb generation under low LET using stochastic models based on the Poisson distribution and the binomial distribution.

Research Products

• [Journal Article] セミの羽化と交尾についての確率論的考察 (2011)
  • Author(s): 税所康正
  • Journal Title: 数理解析研究所講究録 Volume: 1751 Pages: 89-94
• [Journal Article] On the Structural Stability of Discretized Burgers' equation with Randomness (2011)
  • Author(s): I. Hataue
  • Journal Title: Information Volume: 14-8 Pages: 2585-2598
  • Peer Reviewed
• [Journal Article] Statistical Scheme via AIC for Evaluating the Optimal Cut Off Level in Fuzzy Clustering (2011)
  • Author(s): S. Kanagawa, K. Shinkai, H. Chung and K. Nagashima
  • Journal Title: Proceedings of the 2011 IEEE International Conference on Fuzzy Systems Volume: 1 Pages: 1568-1571
  • Peer Reviewed
• [Journal Article] Limit theorems of U-statistics for weakly dependent random variables and their applications to change-point problems (2011)
  • Author(s): K. Yoshihara, S. Kanagawa and S. Fukuda
  • Journal Title: Theoreticaland Applied Mechanics Japan Volume: 60 Pages: 399-418
  • Peer Reviewed
• [Journal Article] Limit theorems of U-statistics for weakly dependent random variables and their applications to change-point problems (2011)
  • Author(s): K.Yoshihara, S.Kanagawa, S.Fukuda
  • Journal Title: Theoretical and Applied Mechanics Japan Volume: 60 Pages: 399-418
  • Peer Reviewed
• [Journal Article] Mathematical observations on the relation between eclosion periods and the copulation rate of cicadas (2010)
  • Author(s): Yasumasa Saisho
  • Journal Title: Theoretical and Applied Mechanics Japan Volume: 7-2 Pages: 443-453
  • Peer Reviewed
• [Journal Article] Approximated Solutions of Schrodinger Equations Induced from Nearly Monochromatic Waves (2010)
  • Author(s): S. Kanagawa, T. Nitta, K. Tchizawa
  • Journal Title: Theoretical and Applied Mechanics Japan Volume: 59 Pages: 153-161
  • Peer Reviewed
• [Journal Article] Limit distribution of a one-dimensional reflecting process of jump type (2010)
  • Author(s): Yasumasa Saisho
  • Journal Title: Tokyo J. Math. Volume: 32-1 Pages: 1-17
  • Peer Reviewed
• [Journal Article] Mathematical observations on the relation between eclosion periods and the copulation rate of cicadas (2010)
  • Author(s): Yasumasa Saisho
  • Journal Title: Mathematical Biosciences and Engineering Volume: 7-2 Pages: 443-453
  • Peer Reviewed
• [Journal Article] Mathematical observations on the relation between eclosion periods and the copulation rate of cicadas (2010)
  • Author(s): Yasumasa Saisho
  • Journal Title: Mathematical Biosciences and Engineering 7-2(掲載決定)
  • Peer Reviewed
• [Journal Article] Limit distribution of a one-dimensional reflecting process of jump type (2009)
  • Author(s): Yasumasa Saisho
  • Journal Title: Tokyo J.Math. 32-1 Pages: 1-17
  • Peer Reviewed
• [Presentation] A model of stock prices using a multi-dimensional reflecting Brownian motion described by the Skorohod SDE, AMS Sectional Meeting# 1079, Special Session on Stochastic Analysis and Applications, II (2012)
  • Author(s): S. Kanagawa
  • Organizer: 2012 Spring Southeastern Section Meeting
  • Place of Presentation: University of South Florida, Tampa,米国
• [Presentation] A model of stock prices using a multi-dimensional reflecting Brownian motion described by the Skorohod SDE (2012)
  • Author(s): S.Kanagawa
  • Organizer: AMS Sectional Meeting #1079, Special Session on Stochastic Analysis and Applications, II, 2012 Spring Southeastern Section Meeting
  • Place of Presentation: University of South Florida, Tampa,米国(招待講演)
• [Presentation] Study of Structure of Ensemble Average in Compressible Flow Simulations with Randomness (2011)
  • Author(s): I. Hataue
  • Organizer: 2011 International Conference on Applied and Engineering Mathematics
  • Place of Presentation: Shanghai,中国
  • Year and Date: 2011-10-30
• [Presentation] Nagashima Statistical Scheme via AIC for Evaluating the Optimal Cut Off Level in Fuzzy Clustering (2011)
  • Author(s): S. Kanagawa, K. Shinkai, H. Chung and K.
  • Organizer: IEEE International Conference on Fuzzy Systems
  • Place of Presentation: Taipei,台湾
  • Year and Date: 2011-06-27
• [Presentation] Statistical Scheme via AIC for Evaluating the Optimal Cut Off Level in Fuzzy Clustering (2011)
  • Author(s): S.Kanagawa, K.Shinkai, H.Chung, K.Nagashima
  • Organizer: IEEE International Conference on Fuzzy Systems
  • Place of Presentation: Taipei,台湾
  • Year and Date: 2011-06-27
• [Presentation] 従属確率変数列に対するU-統計量に関する極限定理およびその日経225平均株価分析への応用 (2011)
  • Author(s): 吉原健一, 福田修平, 金川秀也
  • Organizer: 60回理論応用力学講演会
  • Place of Presentation: 東京工業大学
  • Year and Date: 2011-03-10
• [Presentation] 従属確率変数列に対するU-統計量に関する極限定理およびその日経225 平均株価分析への応用 (2011)
  • Author(s): 吉原健一, 福田修平, 金川秀也
  • Organizer: 60回理論応用力学講演会
  • Place of Presentation: 東京工業大学(招待講演)
  • Year and Date: 2011-03-10
• [Presentation] ランダムノイズが周期解に及ぼす影響に関する数値的考察 (2011)
  • Author(s): 畑上到
  • Organizer: 第15回環瀬戸内応用数理研究部会シンポジウム
  • Place of Presentation: 山口東京理科大学(小野田市)
• [Presentation] セミの羽化と交尾についての確率論的考察, 2010年度京都大学数理解 (2010)
  • Author(s): 税所康正
  • Organizer: 析研究所共同利用研究集会第7回「生物数学の理論とその応用
  • Place of Presentation: 京都大学数理解析研究所(京都市)
• [Presentation] DNAの2本鎖切断に関する数理生物学的考察 (2010)
  • Author(s): 税所康正・伊藤敦
  • Organizer: 日本放射線影響学会53回大会
  • Place of Presentation: 京都テルサ(京都市)
• [Presentation] セミの交尾生態に関する数理的考察 (2010)
  • Author(s): 税所康正
  • Organizer: 日本昆虫学会第70回大会
  • Place of Presentation: 山形大学農学部(鶴岡市)
• [Presentation] A New Model Using a Semi-Reflecting Brownian Motion and Its Application to Behavioral Finance, Fourth International Conference on Neural (2010)
  • Author(s): S. Kanagawa
  • Organizer: Parallel & Scientific Computations
  • Place of Presentation: Atlanta, Georgia, U. S. A
• [Presentation] DNAの2本鎖切断に関する数理生物学的考察 (2010)
  • Author(s): 税所康正・伊藤敦
  • Organizer: 日本放射線影響学会53回大会
  • Place of Presentation: 京都テルサ(京都市)(招待講演)
• [Presentation] セミの羽化と交尾についての確率論的考察 (2010)
  • Author(s): 税所康正
  • Organizer: 2010年度京都大学数理解 析研究所共同利用研究集会第7回「生物数学の理論とその応用」
  • Place of Presentation: 京都大学数理解析研究所(京都市)
• [Presentation] A New Model Using a Semi-Reflecting Brownian Motion and Its Application to Behavioral Finance (2010)
  • Author(s): S.Kanagawa
  • Organizer: Fourth International Conference on Neural, Parallel & Scientific Computations
  • Place of Presentation: Atlanta, Georgia, U.S.A.(招待講演)
• [Presentation] 確率論を用いたDNA2本鎖切断生成に関する数理生物学的考察 (2009)
  • Author(s): 伊藤敦・税所康正
  • Organizer: 日本放射線影響学会第52回大会
  • Place of Presentation: 広島市
• [Book] 日本産セミ科図鑑 (2011)
  • Author(s): 林正美・税所康正
  • Total Pages: 224
  • Publisher: 誠文堂新光社
• [Remarks]
  • URL: http://home.hiroshima-u.ac.jp/saisho/index-j.html
• [Remarks]
  • URL: http://home.hiroshima-u.ac.jp/saisho/index-j.html
• [Remarks]
  • URL: http://home.hiroshima-u.ac.jp/saisho/index-j.html
• [Remarks]
  • URL: http://home.hiroshima-u.ac.jp/saisho/index-j.html