2013 Fiscal Year Final Research Report
Multilateral research on infinite dimensional differential operators via stochastic analysis
| Project/Area Number |
23740107
|
|---|
| Research Category |
Grant-in-Aid for Young Scientists (B)
|
| Allocation Type | Multi-year Fund |
|---|
| Research Field |
Basic analysis
|
|---|
| Research Institution | Okayama University |
|---|
Principal Investigator |
KAWABI HIROSHI 岡山大学, 自然科学研究科, 准教授 (80432904)
|
|---|
| Project Period (FY) |
2011 – 2013
|
| Keywords | 確率解析 / 経路空間 / 微分作用素 / 一意性定理 / 確率偏微分方程式 / Rough Path理論 / 推移確率 / 漸近挙動 |
|---|
| Research Abstract |
I mainly studied uniqueness problems of differential operators and corresponding stochastic dynamics on infinite dimensional spaces via stochastic analysis. In particular, I proved strong uniqueness of Dirichlet operators for Gibbs measures which appear in quantum field theory and constructed a unique solution to the corresponding stochastic PDE by using Dirichlet form theory. Besides, I studied precise asymptotic behavior (i.e., the method of stationary phase) of some oscillatory functional integrals by combining Rough Path theory with Malliavin calculus. Motivated by this study of the stationary phase method, I also obtained an explicit effect of non-symmetry on the long time asymptotic behavior for a class of non-symmetric random walks on the triangular lattice.
|
