2009 Fiscal Year Final Research Report
Dirichlet Forms and Stochastic Analysis of Symmetric Markov Processes
| Project/Area Number |
18340033
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Tohoku University |
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Principal Investigator |
TAKEDA Masayoshi Tohoku University, 大学院・理学研究科, 教授 (30179650)
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| Co-Investigator(Renkei-kenkyūsha) |
HATTORI Tetstuya 慶応大学, 経済学部, 教授 (10180902)
HATTORI Tetstuya 広島大学, 大学院・工学研究科, 教授 (70229657)
KUWAE Kazuhiro 熊本大学, 工学部, 教授 (80243814)
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| Project Period (FY) |
2006 – 2009
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| Keywords | ディリクレ形式 / マルコフ過程 / 大偏差原理 |
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| Research Abstract |
The theory of Dirichlet forms is an L^2-theory, while the theory of Markov processes is, in a sense, an L^1-theory. To bridge this gap, we study the L^p-independence of growth bounds of Markov semigroups, more generally, of generalized Feynman-Kac (Schroedinger) semigroups. A key idea for the proof of the L^p-independence is to employ arguments in the Donsker-Varadhan large deviation theory. The L^p-independence enables us to control L^∞-properties of the symmetric Markov process ; in fact, we can state, in terms of the bottom of L^2-spectrum, a necessary and sufficient conditions for the integrability of Feynman-Kac functionals and for the stability of Gaussian both side estimates of Schroedinger heat kernels.
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