Application of two-dimensional fluctuation theory to mathematical physics and actuarial science

• Project/Area Number: 22540127
• 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: Kyoto Institute of Technology (2011-2012); Osaka University (2010)
• Principal Investigator: ISOZAKI Yasuki 京都工芸繊維大学, 工芸科学研究科, 准教授 (90273573)
• Project Period (FY): 2010 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000); Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• Keywords: 確率論 / 揺動理論 / 更新理論 / ブラウン運動 / ポテンシャル理論

Research Abstract

We studied the joint distribution concerning the first hitting time/place of a half line or parallel two lines in the plane by a two-dimensional stable Levy process. We studied the weak convergence of a family of probability distributions arising in the renewal theory. We obtained a better error term for the asymptotic behavior of the renewal density. We characterized the “Brownian motion reflecting at the integer-valued ratchet” by the family of equations of the Skorohod type.

Research Products

• [Journal Article] A property of the Fourier transform of probability measures on the real line related to the renewal theorem (2012)
  • Author(s): 磯崎泰樹
  • Journal Title: Proceedings of the Japan Academy Volume: 88 Ser..A Pages: 152-155
  • NAID: 40019504472
  • Peer Reviewed
• [Journal Article] A property of the Fourier transform of probability measures on the real line related to the renewal theorem (2012)
  • Author(s): Yasuki Isozaki
  • Journal Title: Proceedings of the Japan Academy, Ser.A Volume: 88 Pages: 152-155
  • NAID: 40019504472
  • Peer Reviewed
• [Journal Article] Hitting of a line or a half-line in the plane by two-dimensional symmetric stable Levy processes (2011)
  • Author(s): 磯崎泰樹
  • Journal Title: Stochastic Processes and their Applications Volume: 121
  • Peer Reviewed
• [Journal Article] Hitting of a line by two-dimensional symmetric stable Levy processes : an approach based on modified resolvents (2010)
  • Author(s): 磯崎泰樹
  • Journal Title: 京都大学数理解析研究所講究録 Volume: 1672 Pages: 159-176
• [Presentation] 1/cosh(x)の部分分数展開の確率論的解釈と拡張 (2011)
  • Author(s): 磯崎泰樹
  • Organizer: 大阪大学理学研究科数学専攻談話会
  • Place of Presentation: 、大阪大学理学研究科数学専攻
  • Year and Date: 2011-01-31
• [Presentation] 1/cosh(x)の部分分数展開の確率論的解釈と拡張 (2011)
  • Author(s): 磯崎泰樹
  • Organizer: 大阪大学 数学教室 談話会
  • Place of Presentation: 大阪大学理学研究科
  • Year and Date: 2011-01-31