| Project/Area Number |
03302010
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| Research Category |
Grant-in-Aid for Co-operative Research (A)
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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 | Osaka University |
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Principal Investigator |
FUKUSHIMA Masatoshi Osaka Univ.,Fac of Eng Sci.,Professor, 基礎工学部, 教授 (90015503)
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| Co-Investigator(Kenkyū-buntansha) |
MAEJIMA Shin Keio Univ.,Fac Sci Tech.,Professor, 理工学部, 教授 (90051846)
FUNAKI Naohisa Nagoya Univ.,Fac Sci.,Professor, 理学部, 教授 (60112174)
NISIO Makiko Kobe Univ.,Fac Sci.,Professor, 理学部, 教授 (80030758)
NAKAO Shintaro Kanazawa Univ.,Fac Sci.,Professor, 理学部, 教授 (90030783)
KUSUOKA Shigeo Kyoto Univ.,RIMS,Associate Professor, 数理解析研究所, 助教授 (00114463)
杉田 洋 九州大学, 教養部, 助教授 (50192125)
竹中 茂夫 広島大学, 理学部, 助教授 (80022680)
浜地 敏弘 九州大学, 教養部, 教授 (20037253)
木上 淳 大阪大学, 数養部, 講師 (90202035)
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| Project Period (FY) |
1991 – 1992
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| Project Status |
Completed (Fiscal Year 1992)
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| Budget Amount *help |
¥17,300,000 (Direct Cost: ¥17,300,000)
Fiscal Year 1992: ¥9,700,000 (Direct Cost: ¥9,700,000)
Fiscal Year 1991: ¥7,600,000 (Direct Cost: ¥7,600,000)
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| Keywords | stochastic analysis / Malliavin calculus / analysis on fractals / Dirichlet forms / stable random field / quantum chaos / stochastic control / finance theory / 正則関数 / 符号化定理 / 拡散過程 / ウィナ-・リ-マン多様体 / ジュリア集合 / エルゴ-ド的流 / ディリクレ形成 |
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| Research Abstract |
This co-operative research aims at a systematic development of stochastic analysis both in theory and applications. To this end, the chief investigator and investigators organized 14 symposiums of four different categories in two years:
a)Stochastic analysis in mathematics: infinite dimensional analysis, finite dimensional analysis and Markov processes
b)Mathematics fractal sets based on stochastic analysis
c)Applications of stochastic analysis to other fields: Mathematical physics, engineering science and economics
d)Stochastic analysis within probability theory: specific investigations on probability distributions and random fields
Each symposium contained general reviews on recent progress, reports on new results and discussions for future developments. Specific achievements by this research in each category are:
a)development in Malliavin calculus and theory of Dirichlet forms
b)progress on diffusion processes and spectral analysis on fractal sets
c)mathematical progress on quantum chaos, control theory, information theory and finance theory
d)new understanding on unimodal distributions and stable random fields
We had two big conferences in which more than 150 mathematicians participated and the above four categories are mixed together to create a new understanding on the depth and width of stochastic analysis both in theory and applications and on its promising future.
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