Stochastic analysis for coagulation-fragmentation processes
| Project/Area Number |
26400142
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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 | Saga University |
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Principal Investigator |
Handa Kenji 佐賀大学, 理工学部, 教授 (10238214)
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| Project Period (FY) |
2014-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 凝結 / 分裂 / 相関関数 / 可逆分布 / 定常分布 / 点過程 / Poisson-Dirichlet分布 / 一意性 / split / merge / 区間分割 |
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| Outline of Final Research Achievements |
The phenomena of coagulation and fragmentation are widely observed in nature. It is typical that the mathematical analysis for them is based on a nonlinear equation regarded as `the fundamental equation'. However, the previous studies are obliged to made the constraint on the growth order of the coagulation and fragmentation rates. In this research, introducing suitably a microscopic model describing random coagulation and fragmentation, and then taking a proper scaling limit, we have derived a certain class of coagulation-fragmentation equations with rates which are not necessarily satisfying the growth order previously required.
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| Academic Significance and Societal Importance of the Research Achievements |
自然現象のみならず社会現象の記述・理解には数学は欠かせない．本研究での対象は，少なくとも歴史的には物理的背景を主な動機として持つが，数学的記述そのものは非常に汎用性が高いため，例えば生物等の社会的集団の合併・分割といった現象の研究においても，本研究で議論したモデル（微視的確率モデルおよび導出された非線形方程式で記述されるモデル）は一定の役割を担うことが可能となる場合があると期待される．
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Report
(6 results)
Research Products
(8 results)
