2010 Fiscal Year Final Research Report
New development of theory of stochastic processes via penalisations
| Project/Area Number |
21740069
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Kyoto University |
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Principal Investigator |
YANO Yuko Kyoto University, 大学院・理学研究科, 助教 (10337462)
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| Project Period (FY) |
2009 – 2010
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| Keywords | 確率論 / 確率過程論 / 処罰問題 / 極限定理 / 安定過程 / レヴィ過程 / 拡散過程 |
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| Research Abstract |
I studied supremum penalisation for stable Levy processes and obtained the following results: I solved the problem partially by using the excursion theory for reflected processes and the scaling property (joint work with K. Yano and M. Yor) ; I succeeded in constructing by harmonic transforms for Levy processes the sigma-finite measure which unifies the supremum penalisations. Meanwhile, in some connection with occupation time penalisation, I obtained the following : I determined the asymptotic behavior of the density of the law of the occupation time for a diffusion on fractals (joint work with N. Kajino, T. Kumagai, M. Kwasnicki, and S. Watanabe).
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