2013 Fiscal Year Final Research Report
Functional analytic study on asymptotic properties of Markov processes
| Project/Area Number |
22340024
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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 東北大学, 理学(系)研究科(研究院), 教授 (30179650)
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| Co-Investigator(Renkei-kenkyūsha) |
KUWAE Kazuhiro 熊本大学, 大学院・自然科学研究科, 教授 (80243814)
SHIOZAWA Yuichi 岡山大学, 大学院・自然科学研究科, 准教授 (60454518)
TSUCHIDA Kameharu 防衛大学校, 数学教育室, 講師 (80466523)
TAWARA Yoshihiro 長岡工業高等専門学校, 一般教育科, 准教授 (00567901)
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Keywords | ディリクレ形式 / 対称マルコフ過程 / 大偏差原理 / 加法汎関数 / スペクトル下限 |
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| Research Abstract |
The theory of Dirichlet forms has been developed as a useful tool for studying symmetric Markov processes. The theory of Dirichlet forms is an L-2-theory, and which is a reason why the theory is suitable for treating singular Markov processes. However, the theory of Markov processes is, in a sense, an L-1-theory. To bridge this gap, we prove the L-p-independence of growth bounds of Markov semi-groups under the conditions for the Markov processes to be strong Feller and to be tight. By applying the L-p-independence to time changed Markov processes, we show the exponential integrability of positive continuous additive functionals (PCAF's in short) and the large deviation principle of PCAF's. Moreover, we give a necessary and sufficient condition for heat kernel estimates being stable by perturbation of potential terms.
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