Superposition of diffusion processes on a high-dimensional Tube

• Project/Area Number: 26800060
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Basic analysis
• Research Institution: Nara Women's University
• Principal Investigator: TAKEMURA TOMOKO 奈良女子大学, 自然科学系, 助教 (40598140)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Project Status: Completed (Fiscal Year 2017)
• Budget Amount: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000); Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
• Keywords: 収束定理 / 拡散過程 / 斜積拡散過程 / ディリクレ形式 / ブラウン運動 / 高次元チューブ / skew product / diffusion process / limit theorem / Dirichlet Form / jump rate / brownian motion / Bessel process / 斜積 / 極限定理 / 局所時間

Outline of Final Research Achievements

We considered Limit theorems for diffusion processes on a high-dimensional tube. The sequence of diffusion processes are given by direct product diffusion processes D and Y and the time changed diffusion processes where D is a one-dimensional diffusion process and Y is a skew product diffusion of a one-dimensional diffusion process R and d-1 dimensional spherical Brownian motion by means of positive continuous additive functional of R.
We show a limit theorem for a sequence of time changed process under some assumptions for underlying measures and we also obtained concrete expressions of the Dirichlet forms corresponding to time changed processes, which may be of non-local type on a tube caused by degeneracy of the underlying measures.

Research Products

• [Journal Article] Jump measure densities corresponding to Brownian motion on annulus (2018)
  • Author(s): Tomoko TAKEMURA
  • Journal Title: Ann. Reports of Graduate School of Humanities and Sciences, Nara Women's University Volume: 33
  • NAID: 120006658270
  • Peer Reviewed / Open Access
• [Journal Article] Exponent of inverse local time for harmonic transformed process (2016)
  • Author(s): Tomoko TAKEMURA and Matsuyo TOMISAKI
  • Journal Title: Ann. Reports of Graduate School of Humanities and Sciences, Nara Women's University Volume: 31 Pages: 127-138
  • NAID: 40020830362
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Presentation] チューブ内を運動する拡散過程の極限定理 (2018)
  • Author(s): 嶽村 智子
  • Organizer: マルコフ過程とその周辺
• [Presentation] Convergence of diffusion processes in a tube (2018)
  • Author(s): 嶽村 智子
  • Organizer: 日本数学会 2018年度年会
• [Presentation] Convergence for diffusions in balls whose diameter changes (2017)
  • Author(s): Tomoko TAKEMURA
  • Organizer: KWMS International Conference 2017
  • Int'l Joint Research
• [Presentation] Exponent of Levy processes corresponding to inverse local time for harmonic transformed diffusion processes (2016)
  • Author(s): Tomoko TAKEMURA
  • Organizer: World Congress in Probability and Statistics
  • Place of Presentation: Fields institute, Toronto
  • Int'l Joint Research