Sample path analysis for symmetric Markov processes and Dirichlet forms
| Project/Area Number |
26400135
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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 | Okayama University |
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Principal Investigator |
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 対称マルコフ過程 / ディリクレ形式 / レート関数 / 保存性 / 非再帰性 / 分枝ブラウン運動 / マルコフ過程 / ブラウン運動 / 再帰性 / 脱出レート |
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| Outline of Final Research Achievements |
We developed the sample path analysis for symmetric Markov processes generated by regular Dirichlet forms. We first gave estimates on the speed of particles escaping to infinity (lower escape rate) under the condition on the volume growth or heat kernel. We further proved that some integral in the estimates above expresses the decay rate of some tail probability related to the lower escape rate. We next determined the escape rate of the Brownian motions on hyperbolic spaces. We finally proved that for branching Brownian motions on the Euclidean space, the spread rate is determined by the principal eigenvalue of some Schro"dinger type operator under some suitable condition.
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Report
(4 results)
Research Products
(25 results)
