Analysis of Stochastic Processes on the Adeles

2009 Fiscal Year Self-evaluation Report

• Project/Area Number: 19740055
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Keio University
• Principal Investigator: YASUDA Kumi Keio University, 商学部, 准教授 (40284484)
• Project Period (FY): 2007 – 2010
• Keywords: アデール環 / マルコフ過程 / オイラー積

Research Abstract

2007～2008年度に、アデール上のマルコフ過程の構成と、その特性量の計算を行う.
2009年度にマルコフ過程を用いたゼータ関数やオイラー積の表示について研究する.
2010年度には,得られた表示式を応用した関数解析を進める.

Research Products

• [Journal Article] Markov processes on R^2 with ultrametric jumps (2010)
  • Author(s): Kumi Yasuda
  • Journal Title: 数理解析研究所講究録 1672巻 Pages: 111
• [Journal Article] Markov processes on the adeles (2008)
  • Author(s): Kumi Yasuda
  • Journal Title: 数理解析研究所講究録 1590巻 Pages: 120-125
• [Journal Article] Markov processes on the adeles and representations of Euler products
  • Author(s): Kumi Yasuda
  • Journal Title: Journal of Theoretical Probability (掲載決定)
  • Peer Reviewed
• [Presentation] Markov processes on the adeles and applications (2010)
  • Author(s): Kumi Yasuda
  • Organizer: 神楽坂解析セミナー
  • Place of Presentation: 東京理科大学理学部
  • Year and Date: 2010-03-18
• [Presentation] Markov processes on the adeles and representations of Riemann zeta function (2010)
  • Author(s): Kumi Yasuda
  • Organizer: Seminar on Mathematics
  • Place of Presentation: Opole University(Poland).
  • Year and Date: 2010-03-11
• [Presentation] p進値確率過程について, ヤングサマーセミナー2009 (2009)
  • Author(s): 安田公美
  • Place of Presentation: 国民宿舎つづらお荘
  • Year and Date: 20090818-20090822
• [Presentation] Q_pのはなし (2009)
  • Author(s): 安田公美
  • Organizer: 研究集会「確率解析の理論と応用- さよなら箱崎」
  • Place of Presentation: 九州大学数理学研究院
  • Year and Date: 20090724-20090725
• [Presentation] Markov processes on R^2 with ultrametric jumps, Stochastic Analysis of Jump Processes (2009)
  • Author(s): Kumi Yasuda
  • Organizer: 数理研研究集会
  • Place of Presentation: 京都大学理学部
  • Year and Date: 20090708-20090709
• [Presentation] Markov processes on adeles, Number Theory and Probability (2007)
  • Author(s): Kumi Yasuda
  • Organizer: Workshop
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 20071015-20071016