Toward a foundation of leafwise stochastic calculus on foliated spaces
| Project/Area Number |
26610024
|
|---|
| Research Category |
Grant-in-Aid for Challenging Exploratory Research
|
| Allocation Type | Multi-year Fund |
|---|
| Research Field |
Basic analysis
|
|---|
| Research Institution | Osaka University |
|---|
Principal Investigator |
|
|---|
| Co-Investigator(Renkei-kenkyūsha) |
SUGITA Hiroshi 大阪大学, 大学院理学研究科, 教授 (50192125)
HIBI Masanori 京都大学, 大学院理学研究科, 教授 (40303888)
|
|---|
| Research Collaborator |
SUZAKI Kiyotaka
TOKUNAGA Yusuke
IKEDA Takuya
SUZUKI Shintaro
|
|---|
| Project Period (FY) |
2014-04-01 – 2017-03-31
|
| Project Status |
Completed (Fiscal Year 2016)
|
| Budget Amount *help |
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
|
|---|
| Keywords | 確率解析 / ブラウン運動 / 葉層付き空間 / 各葉拡散過程 / 中心極限定理 / 混合型中心極限定理 |
|---|
| Outline of Final Research Achievements |
A foliated space is a family of manifolds each of which is called a leaf satisfying some geometric conditions. A leafwise Brownian motion on a foliated space is a diffusion process obtained by combining Brownian motions on leaves provided that each leaf is insulated from the others. We tried to establish a foundation of stochastic analysis on foliated space via the leafwise Brownian motion. There are many processes in order to finish it. We verified that most processes are finished. But a few of them are still in construction because of technical difficulties. As by-products we obtain a several results including a central limit theorem for leafwise Brownian motions on mapping tori.
|
Report
(4 results)
Research Products
(6 results)
