| Project/Area Number |
14540101
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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 | SAITAMA UNIVERSITY |
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Principal Investigator |
DOKU Isamu SAITAMA UNIVERSITY, Faculty of Education, Professor, 教育学部, 教授 (60207686)
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| Project Period (FY) |
2002 – 2005
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| Project Status |
Completed (Fiscal Year 2005)
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| Budget Amount *help |
¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 2005: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2004: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2003: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2002: ¥900,000 (Direct Cost: ¥900,000)
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| Keywords | Measure-valued stochastic processes / Branching processes / Random measures / Interactive particle systems / Immigration superprocesses / Scaling / Limit theorem / Convergence problem / 測定値確率過程 / ランダム測定 / 超ブラウン運動 / 確率偏微分方程式 / 法則の絶対連続性 / 測度値過程 / 分枝マルコフ過程 / 特異分枝率 / 非線形方程式 / 許容的加法的汎関数 / 超過程 / 速度値過程 / 特異分岐率 |
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| Research Abstract |
Our main interest is a class of singular superprocesses. First of all we proved that there exists a unique measure-valued branching Markov process for a wider class of singular branching rates, which includes a Fleischmann-Muller superprocess with hyperbolic branching rate. We also showed the regularity of their paths. Then we derived a sufficient condition for such a class of superprocesses to possess the finite time extinction property. Moreover, we extended those results to a class of generalized superprocesses with diffusion-like spatial motion.
Next we tried to obtain a generalization of Dawson-Li-Zhon convergence result to SCSM. Actually we considered a more complicated class of superprocesses with immigration, and proved a limit theorem that rescaled immigration superprocesses converges to a SCSM in the sense of distribution on the space of measure-valued continuous paths. Now we are planning a new research project that we aim at deriving a new type of limit theorem, where a superprocess more generalized than SCSM arises as a rescaled limit.
Furthermore, we proved an existence and uniqueness theorem for weak solution to various kinds of stochastic equations associated with such a class of singular superprocesses. For a specific example, we showed absolute continuity of the law of solution by applying stochastic analysis.
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