Extensions of reflecting Markov processes on unbounded domains
| Project/Area Number |
22540125
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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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| Project Period (FY) |
2010 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2012: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Keywords | 無限錐 / 反射壁ブラウン運動 / 多重連結領域 / 小松・レブナー微分方程式 / かがりブラウン運動 / SKLE / 1次元極小拡散過程 / 対称性 / 対称拡散拡張 / ２次元かがりブラウン運動 / 小松レブナー方程式 / ランダム曲線 / SLE / 等角不変 / 確率微分方程式 / 3次元反射壁ブラウン運動 / 2次元縢りブラウン運動 / 小松-Loewner微分方程式 / 等角写像 / 1次元拡散過程 / 一般境界条件 / 無限錘 / 対称マルコフ的拡張 / 非対称安定型過程 / 非対称ディリクレ形式 / 小松-Leowner方程式 |
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| Research Abstract |
1. The time changed reflecting Brownian motion on a 3-space consisting of two infinite cones is shown to admit 4 and only 4 possible symmetric Markovian extensions.
2. The Komatu-Loewner differential equation for a multiply connected planar domain is derived by the Brownian motion with darning (BMD). The notion of stochastic Loewner evolution (SLE) for simply connected domains is extended to multiply connected domains as stochastic Komatu-Loewner evolution (SKLE).
3. The minimal diffusion on an interval is shown to be symmetric for the canonical measure and all its symmetric diffusion extensions are identified in relation to Ito-McKean’ s theory. As a result, the one-dimensional diffusions with general boundary conditions can be directly constructed by means of regular Dirichlet forms.
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Report
(4 results)
Research Products
(19 results)
