A new development of stochastic differential geometry associated with degenerate differential operators

• Project/Area Number: 24540178
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Kyushu University
• Principal Investigator: TANIGUCHI Setsuo 九州大学, 基幹教育院, 教授 (70155208)
• Co-Investigator(Renkei-kenkyūsha): MATSUMOTO Hiroyuki 青山学院大学, 理工学部, 教授 (00190538) ; SHIRAI Tomoyuki 九州大学, マス・フォア・インダストリ研究所, 教授 (70302932) ; UEMURA Hideaki 愛知教育大学, 教育学部, 教授 (30203483)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Project Status: Completed (Fiscal Year 2014)
• Budget Amount: ¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000); Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2013: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000); Fiscal Year 2012: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
• Keywords: CR-多様体 / CR-ブラウン運動 / 熱核 / 確率微分幾何 / Malliavin解析

Outline of Final Research Achievements

A diffusion process generated by a sub-Laplacian, which is a real part of the Kohn-Rossi Laplacian on a CR-manifold, is constructed in a globally geometrical manner by extending the Elles-Elworthy-Malliavin approach to the Brownian motion on a Riemannian manifold. Using the diffusion process (CR-Brownian motion), the heat equation and the Dirichlet problem associated with the sub-Laplacian are investigated in a stochastically analytic manner.

Research Products

• [Journal Article] A NEW CLASS OF AMPLITUDE FUNCTIONS FOR THE STATIONARY PHASE METHOD ON AN ABSTRACT WIENER SPACE (2015)
  • Author(s): Setsuo Taniguchi
  • Journal Title: Kyushu Journal of Mathematics Volume: 69 Issue: 1 Pages: 219-228
  • DOI: 10.2206/kyushujm.69.219
  • NAID: 130005076143
  • ISSN: 1340-6116, 1883-2032
  • Peer Reviewed / Acknowledgement Compliant
• [Presentation] Diffuison processes on CR-manifolds (2014)
  • Author(s): Setsuo Taniguchi
  • Organizer: UK-Japan stochastic analysis school 2014
  • Place of Presentation: Warwick University
  • Year and Date: 2014-09-05
• [Presentation] Rolling manifolds
  • Author(s): 谷口説男
  • Organizer: 研究集会「確率解析」
  • Place of Presentation: 京都大学数理解析研究所
  • Invited
• [Remarks] Welcome to S. Taniguchi's Wiki!
  • URL: https://mserve.artsci.kyushu-u.ac.jp/groups/s_taniguchi/