2002 Fiscal Year Final Research Report Summary
Stochastic Calculus for symmetric diffusion processes and its applications
| Project/Area Number |
13640143
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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 | Kansai University |
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Principal Investigator |
FUKUSHIMA Masatoshi Kansai Univ., Faculty of Engineering, Prof., 工学部, 教授 (90015503)
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| Co-Investigator(Kenkyū-buntansha) |
UEMURA Toshihiro Kobe Univ. of Commerce, Faculty of Commerce and economy, Lecturer, 商経学部, 講師 (30285332)
KUSUDA Masaharu Kansai Univ., Faculty of Engineering, Prof., 工学部, 教授 (80195437)
KURISU Tadashi Kansai Univ., Faculty of Engineering, Prof., 工学部, 教授 (00029159)
MAEDA Tooru Kansai Univ., Faculty of Engineering, Associate Prof., 工学部, 助教授 (20199623)
HIRASHIMA Yasumasa Kansai Univ., Faculty of Engineering, Associate Prof., 工学部, 助教授 (80047399)
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| Project Period (FY) |
2001 – 2002
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| Keywords | symmetric diffusion / abstract Wiener space / stochastic stopping game / isoperimetric inequality / ultracontractivity / time changed process / d-set / Besov space |
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| Research Abstract |
The head investigator has succeeded to apply the stochastic calculus of symmetric diffusions to different subjects with researchers in different countries, and the results have been published in three international journals. The head investigator collaborates with investigators to develop potential theory for a general function space with contractive p-norm and apply it to the study of Besov spaces on d-sets and associated jump type Markov processes. Furthermore, for a general symmetric Markov process, a capacitary isoperimetric inequality of a measure is shown to be equivalent to the ultracontractivity of the time changed process on the support of measure. The results are being published as three papers in international journals.
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Research Products
(12 results)
