Boundary problem of Markov processes and point processes
| Project/Area Number |
19540125
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Osaka University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
会田 茂樹 大阪大学, 大学院・基礎工学研究科, 教授 (90222455)
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| Project Period (FY) |
2007 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2009: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2008: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2007: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Keywords | 確率論 / マルコフ過程 / 点過程 / 対称マルコフ過程 / 反射ディリクレ形式 / 1次元拡散過程 / 多次元反射壁ブラウン運動 / 時間変更 / 無限錘領域 / 対称拡大 / 2点拡張 / 生成作用素 / flux / 付加条件 / レゾルベント分解 / 1点拡張 / 一意拡張 / 境界問題 / ポアッソン点過程 / フェラー測度 / レゾルベント / フラックス / 部分過程 / 飛躍測度 |
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| Research Abstract |
Given a Markov process X with a weak dual process and countable boundary points, all possible Markovian extensions of X beyond its life time preserving the weak duality are characterized in terms of intrinsic quantities for X called Feller measures and independent parameters of killing and jumps on the boundary. Such an extension of X is constructed by repeating one point extensions by means of Poisson point processes of excursions.
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Report
(4 results)
Research Products
(25 results)
