| Project/Area Number |
15K11993
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Statistical science
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| Research Institution | University of Tsukuba |
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Principal Investigator |
KONNO Hidetoshi 筑波大学, システム情報系(名誉教授), 名誉教授 (20134207)
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| Research Collaborator |
TAMURA Yoshiyasu
PASZIT Imre
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 応用確率過程解析 / ホインの微分方程式 / 非平衡系の生成・死滅過程 / 非線形確率過程 / 長期記憶効果 / 位相特異点ダイナミクス / 複雑系のダイナミクス / マスター方程式 / フォッカー・プランク方程式 |
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| Outline of Final Research Achievements |
In the classical applied probability theory and analysis, mathematical analysis can be possible only when Markov stochastic models can be reduced to problems of solving Gauss’s hyper-geometric differential equation (GHGDE). In the present study, we developed `` a method of Heun’s differential equation (HDE)’’ to treat a class of non-Markov, non-Gaussian stochastic models which are related to solving problems beyond the class of GHGDE. The main theoretical methods covers for (1) solving a class of fractional master equation; (2) solving a class of fractional Fokker-Planck equation with third order nonlinear in the regression term and second order in the diffusion term; (3) generating superstatistical fractional Poisson process, a class of stochastic process beyond HDE. Applied examples in the real world are shown with their developed methods.
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