2012 Fiscal Year Final Research Report
Non regular limits of one-dimensional generalized diffusion processes
| Project/Area Number |
22540132
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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 | Nara Women's University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
IIZUKA Masaru 九州歯科大学, 歯学部, 准教授 (20202830)
MORITOH Yumi 奈良女子大学, 理学部, 特任助教 (80611128)
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| Project Period (FY) |
2010 – 2012
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| Keywords | 広義拡散過程 / 双一般化拡散過程 / 出生死滅過程 / モラン・モデル / 調和変換 |
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| Research Abstract |
We considered the phenomena where we have non regular limits of one-dimensional generalized diffusion processes. When the limit of scale functions and that of speed measure functions have common discontinuous points, we proved the convergence of transition probabilities and showed that the limit process can be a one-dimensional bi-generalized diffusion process, by means of convergence of Green functions. We also investigated the effect of boundary conditions on harmonic transform of one-dimensional generalized diffusion processes. Further we showed some limit theorems for Moran model in population genetics.
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