2009 Fiscal Year Final Research Report
Studies on several problems on infinitely divisible processes and infinitely divisible distributions
| Project/Area Number |
19340025
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 | Keio University |
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Principal Investigator |
MAEJIMA Makoto Keio University, 理工学部, 教授 (90051846)
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| Co-Investigator(Kenkyū-buntansha) |
NAKADA Hitoshi 慶應義塾大学, 理工学部, 教授 (40118980)
TAMURA Yozo 慶應義塾大学, 理工学部, 准教授 (50171905)
YASUDA Kumi 慶應義塾大学, 商学部, 准教授 (40284484)
SUZUKI Yuki 慶應義塾大学, 医学部, 講師 (30286645)
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| Project Period (FY) |
2007 – 2009
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| Keywords | 無限分解可能過程 / 無限分解可能分布 / レヴィ過程 / レヴィ測度 / オルンシュタイン・ウーレンベック過程 |
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| Research Abstract |
Subclasses of infinitely divisible distributions are characterized as ranges of stochastic integral mappings with respect to Levy processes. There was a conjecture that the limiting classes obtained by the iteration of such mappings are identical to the closure of the class of stable distributions for many mappings. We succeeded to show that the conjecture is true. Further, we solved one problem unsolved for long time that is a characterization of semi-selfdecomposable distribution by a stochastic integral mapping with Levy processes. In addition to those, we solved many related problems and found many new ideas for the further studies.
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