Progress of fundamentals of excursion theory and development of its novel applications
| Project/Area Number |
26800058
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Basic analysis
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| Research Institution | Kyoto University |
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Principal Investigator |
YANO Kouji 京都大学, 理学研究科, 准教授 (80467646)
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| Research Collaborator |
NOBA Kei 京都大学, 大学院理学研究科
YAMAZAKI Kazutoshi 関西大学, システム理工学部, 准教授 (50554937)
YANO Yuko 京都産業大学, 理学部, 教授 (10337462)
SERA Toru 京都大学, 大学院理学研究科
ITO Yu 京都産業大学, 理学部, 助教 (70779214)
HASEBE Takahiro 北海道大学, 大学院理学研究院, 准教授 (00633166)
SAKUMA Noriyoshi 愛知教育大学, 教育学部, 講師 (70610187)
SATO Yuzuru 北海道大学, 電子科学研究所, 准教授 (30342794)
SUMI Hiroki 京都大学, 大学院人間・環境学研究科, 教授 (40313324)
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 周遊理論 / 確率過程論 |
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| Outline of Final Research Achievements |
I have made with the help of collaborators new developments of excursion theory from the three viewpoints as follows. (1) We proposed a theory of generalized refracted processes coming from two spectrally negative Levy processes and obtained remarkable results about generalization of classical exit problems as well as compound Poisson approximation of the refracted processes. (2) We established a general theory of functional limit theorem via convergence of excursions and deduced homogenization limit theorem of jumping-in processes. We proposed penalisation problems with various random clocks and succeeded in establishing a profound general theory of local time penalisations. (3) We generalized a known theory of arcsine laws of occupation times for infinite ergodic transforms of mapping dynamical systems with indifferent fixed points by enhancing it to a limit theorem of joint distributions based on the theory of multiray diffusions.
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Report
(5 results)
Research Products
(41 results)
