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

2014 Fiscal Year Final Research Report

• 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
• 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.

Free Research Field

確率解析