Runge-Kutta methods for stochastic differential equations

2009 Fiscal Year Self-evaluation Report

• Project/Area Number: 19540139
• 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: Kyushu Institute of Technology
• Principal Investigator: KOMORI Yoshio Kyushu Institute of Technology, 大学院・情報工学研究院, 助教 (20285430)
• Project Period (FY): 2007 – 2010
• Keywords: 数値数学

Research Abstract

研究目標は,本研究代表者が提案した確率Runge-Kutta(SRK)族(http://dx.doi.org/10.1016/j.apnum.2006.02.002)を基に様々なSRK法を考察し,SRKスキームを充実させることである.具体的には以下の通りである.
(1)弱い意味の近似解を与える陰的SRKスキームの導出.
(2)ドリフト係数についてのみ陰的あるいは半陰的であるdrift-implicit SRKスキームの導出.
(3)数値的安定性に優れた陽的SRKスキームの導出.
(4)少ないシミュレーション回数で良い近似を与える効率的なSRKスキームの導出.

Research Products

• [Journal Article] Weak first-or second-order implicit Runge-Kutta methods for stochastic differential equations with a scalar Wiener process (2008)
  • Author(s): Yoshio Komori
  • Journal Title: Journal of Computational and Applied Mathematics Vol.217 Pages: 166-179
  • URL: http://ds.lib.kyutech.ac.jp/dspace/handle/10228/446
  • Peer Reviewed
• [Presentation] 硬い確率微分方程式に対するチェビシェフ法 (2009)
  • Author(s): Kevin Burrage, Yoshio Komori
  • Organizer: 日本応用数理学会2009年度年会
  • Place of Presentation: 大阪大学豊中キャンパス
  • Year and Date: 2009-09-30
• [Presentation] Weak order Chebyshev methods for stiff stochastic differential equations (2009)
  • Author(s): Kevin Burrage, Yoshio Komori(発表者)
  • Organizer: International Conference on Scientific Computational and Differential Equations 2009
  • Place of Presentation: Beijing Friendship Hotel, Beijing, China
  • Year and Date: 2009-05-29
• [Presentation] Weak order drift-implicit Runge-Kutta methods for stochastic differential equations (2008)
  • Author(s): Yoshio Komori
  • Organizer: International Conference of Numerical Analysis and Applied Mathematics 2008
  • Place of Presentation: Kypriotis International Conference Center, Kos, Greece
  • Year and Date: 2008-09-17
• [Presentation] Drift-implicit 確率 Runge-Kutta 法について (2007)
  • Author(s): 小守良雄
  • Organizer: 日本応用数理学会2007年度年会
  • Place of Presentation: 北海道大学工学部
  • Year and Date: 2007-09-17
• [Presentation] Fully implicit stochastic Runge-Kutta methods for stochastic differential equations with a scalar Wiener process (2007)
  • Author(s): Yoshio Komori
  • Organizer: International Conference on Scientific Computational and Differential Equations 2007
  • Place of Presentation: Le Palais du Grand Large, Saint-Malo, France
  • Year and Date: 2007-07-12
• [Remarks]
  • URL: http://galois.ces.kyutech.ac.jp/~komori/index.html