2001 Fiscal Year Final Research Report Summary
Symmetric Markov processes and large deviation theory
| Project/Area Number |
12640099
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Tohoku University |
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Principal Investigator |
TAKEDA Masayoshi Tohoku University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (30179650)
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| Co-Investigator(Kenkyū-buntansha) |
OSHIMA Yuichi Kumamoto University, Faculty of Engineering, 工学部, 教授 (20040404)
TACHIZAWA Kazuya Tohoku University, Graduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (80227090)
TSUTSUMI Yoshiro Tohoku University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (10180027)
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| Project Period (FY) |
2000 – 2001
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| Keywords | Symmetric Markov processes / large deviation / Diricblet form / additive functional |
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| Research Abstract |
The integrability of Feynman-Kac functional is called gaugeability or conditional gaugeability. The conditional gaugeability is closely related to the subcriticality of Schrodinger operators, that is, the existence of the Green function. In this study, we obtained a necessary and sufficient condition for conditional gaugeability; moreover we showed the equivalence between conditional gaugeability and subcriticality of generalized Schrodinger operators. We applied this condition to show the subcriticality of concrete Schrodinger operators; for example, we considered the Schrodinger operator whose potential is the surface measure of sphare. We obtained a necessary and sufficient condition the Schrodinger operator being subcritical in terms of the radius of the sphere. To prove the necessary and sufficient condition for conditional gaugeability, we extended the full large deviation principle of Donsker-Varadhan type to symmetric Markov processes with finite lifetime and applied it to a time changed process of the Brownian motion.
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