Stochastic Analysis on infinite dimensional spaces

2015 Fiscal Year Final Research Report

• Project/Area Number: 24340023
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Partial Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Tohoku University
• Principal Investigator: Aida Shigeki 東北大学, 理学(系)研究科(研究院), 教授 (90222455)
• Co-Investigator(Renkei-kenkyūsha): Shigekawa Ichiro 京都大学, 大学院理学研究科, 教授 (00127234) ; Hino Masanori 大阪大学, 大学院基礎工学研究科, 教授 (40303888) ; Kawabi Hiroshi 岡山大学, 大学院自然科学研究科, 教授 (80432904) ; Inahama Yuzuru 九州大学, 大学院数理学研究院, 教授 (80431998) ; Hiroshima Fumio 九州大学, 大学院数理学研究院, 教授 (00330358) ; Kuwada Kazumasa 東京工業大学, 大学院理工学研究科, 准教授 (30432032) ; Hariya Yuu 東北大学, 大学院理学研究科, 准教授 (20404030)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Keywords: 確率解析 / 無限次元解析 / ラフパス / 確率微分方程式 / スペクトル / 場の量子論

Outline of Final Research Achievements

We studied the spectral property of OU operators on infinite dimensional spaces. This is an infinite dimensional version of the study of semiclassical behaviour
of the spectral gap of the operator. We determined the asymptotic behaviour of the spectral gap of the OU operator on a loop space of the rotationally symmetric Riemannianmanifold by the hessian of the energy function at the geodesic.
Also we studied stochastic differential equations and rough differential equations. We proved that the Wong-Zakai approximation solution of the reflected stochastic differential equation converges to the solution and formulated reflected rough differential equations and proved the existence of the solutions.

Free Research Field

確率論