2018 Fiscal Year Final Research Report
Functional analysis for paths of Markov processes via semi-Dirichlet forms
| Project/Area Number |
15K04941
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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 | Kansai University |
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Principal Investigator |
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| Project Period (FY) |
2015-04-01 – 2019-03-31
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| Keywords | Dirichlet 形式 / マルコフ過程 / 加法汎関数 |
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| Outline of Final Research Achievements |
Global path properties, such as recurrence, transience and conservativeness, of Markov processes associated with Dirichlet forms are obtained in terms of the volume growth of balls with respect to the basic measure and the behaviors at the infinity of the coefficients of the infinitesimal generator associated with the processes. Moreover, we revealed the instability of such global path properties under Mosco’s convergence of Markov processes.
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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 |
`連続的変化'の破綻が起きうる状況において，標本路が連続であるという拡散過程に限らず，不連続な状況を許容したジャンプ拡散過程，あるいは純飛躍型過程をモデル化した解析の研究が必要である現代において，当該研究はその先駆けともいえる研究である．また，拡散係数や，Levy係数などが滑らかでない場合においては，モデル化される確率過程の構成さえ自明ではない．Dirichlet 形式は，そのような場合においても，正則性と呼ばれれる条件さえ満たされれば確率過程が構成できるという優位性がある．
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