2020 Fiscal Year Final Research Report
Analysis of global properties of symmetric Markov processes
| Project/Area Number |
17K05299
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Osaka University |
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Principal Investigator |
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| Project Period (FY) |
2017-04-01 – 2021-03-31
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| Keywords | マルコフ過程 / ディリクレ形式 / 分枝ブラウン運動 |
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| Outline of Final Research Achievements |
In this research project, we characterized the global properties of a jump-type symmetric Markov process and the functional analytic properties of a Markov semigroup in terms of the spatial dimension, and of the coefficients and jumping kernel of the associated Dirichlet form. We further provided a sufficient condition for the LIL-type asymptotic properties of a non-symmetric jump process in terms of the existence of the second moment of the jumping kernel. We also revealed the global properties and the asymptotic properties of the tail distribution for the maximal displacement of a branching Brownian motion.
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| Free Research Field |
確率過程論
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| Academic Significance and Societal Importance of the Research Achievements |
確率過程の長時間挙動の解析は，でたらめさの織り成す現象をとらえることであり，確率論の基本的な研究課題の一つである。本研究成果は，マルコフ過程の長時間挙動に関して，空間非一様性に起因する様々な現象の解析的および定量的特徴づけを与えている。このような特徴づけを通じて，マルコフ過程の大域的性質を詳しく理解できる。本研究成果は確率過程論と解析学との関係によるものであり，解析学の諸分野とも関わりを持つ。
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