2005 Fiscal Year Final Research Report Summary
Large deviations for symmetric Markov processes and Dirichlet forms
| Project/Area Number |
15540103
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
|
|---|
| Research Institution | Tohoku University |
|---|
Principal Investigator |
TAKEDA Masayoshi Tohoku University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (30179650)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
HATTORI Tetsuya Tohoku University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (10180902)
SHIOYA Takashi Tohoku University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (90235507)
|
|---|
| Project Period (FY) |
2003 – 2005
|
| Keywords | Markov process / Dirichlet form / Feynman-Kac functional / time-changed process |
|---|
| Research Abstract |
We proved that the integrability of Feynman-Kac functionals (gaugeability) is equivalent to that the principal eigenvalue of time-changed process is greater than 1, which is also equivalent to the subcriticality of Schroedinger operators. This fact says that the principal eigenvalue of time-changed process accurately measures the size of measures. Using this fact, we obtained three results : The first result is that the ultracontractiyity of Schroedinger semigroups holds if and only if the princilal eigenvalue of time-changed process is greater than 1. The second result is that the expectation of the number of branches hitting a closed set in a branching symmetric stable process is finite if and only if the princilal eigenvalue is greater than 1. The final result is as foolows : Suppose that the heat kernel on a complete Riemannian manifold satisfies the global Gaussian bounds, so called Li-Yau estimate. Then the heat kernel of the Schroedinger operator also possesses the global Gaussian bounds, if and anly if the princilal eigenvalue is greater than 1.
|
Research Products
(12 results)
