| Project/Area Number |
05302012
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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 | TOKYO INSTITUTE OF TECHNOLOGY |
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Principal Investigator |
SHIGA Tokuzo Tokyo Inst.Tech.Appl.Physics Professor, 理学部, 教授 (60025418)
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| Co-Investigator(Kenkyū-buntansha) |
HATTORI Tetsuya Utsunomiya Univ.Information Ass.Professor, 工学部, 助教授 (10180902)
NAGAI Hideo Nagoya Univ. Information & Culture Ass.Professor, 情報文化学部, 助教授 (70110848)
KUBO Izumi Hiroshima Univ. Mathematics Professor, 理学部, 教授 (70022621)
OGURA Yukio Saga Univ. Mathematics Professor, 理工学部, 教授 (00037847)
KOTANI Shin-ichi Osaka Univ. Mathematics Professor, 理学部, 教授 (10025463)
河野 敬雄 京都大学, 総合人間学部, 教授 (90028134)
竹田 雅好 大阪大学, 基礎工学部, 助教授 (30179650)
松本 裕行 岐阜大学, 教養部, 助教授 (00190538)
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| Project Period (FY) |
1994
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| Project Status |
Completed (Fiscal Year 1994)
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| Budget Amount *help |
¥18,500,000 (Direct Cost: ¥18,500,000)
Fiscal Year 1994: ¥9,100,000 (Direct Cost: ¥9,100,000)
Fiscal Year 1993: ¥9,400,000 (Direct Cost: ¥9,400,000)
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| Keywords | Probability / Stochastic Analysis / Markov Processes / Ergodic Theory / Infinite Particle Systems / Hydrodynamical Limit / Mathematical Physics / Mathematical Biology / 大偏差原理 / フラクタル / 多様体 / ウィーナー空間 |
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| Research Abstract |
As two years project from 1993 we carried out co-operative research on "Probability Theory and Related Topics" in co-operation with the joint researchers of this project and other researchers of the probability section of the Mathematical Society of Japan. First, aiming at futher development of theory of stochastic analysis which is most fundamental in modern probability theory, we organized two symposiums "Analysis on Wiener space" and "Stochastic Analysis". The former is originated by K.Ito and in the latter one a main theme is Dirichlet space theory due to M.Fukushima. In this field Japan is the leading country, and many pioneering works were produced motivated by these symposiums. We had also symposiums "Analysis related to Markov processes" and "Stochastic Analysis on Manifolds and Large Deviation Theory", which are related to analysis and geometry, jointly with invited analysts and geometricians. Based upon the discussions there new researchs were created. Furthermore, aiming at
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application of stochastic analysis to physics and biology we organized three symposiums "Stochastic Analysis in Physics and Biology", "Fractals and Related Fields" and "Infinite Particles Systems and Hydrodynamical LImit" in cooperation with phycists and biologists, and we could find out several fascinating mathematical problems. It has been proved that stochastic analysis is very powerful in the engineering involving control theory, mathematical economics such as finance theory and mathematical approach in sociology, for which we organized two symposiums "Stochastis Models in Applied Fields" and "Application of Stochastic Analysis". Moreover to discuss new results on miscellaneous problems of probability theory we organized "Gaussian and Stable Processes and their Applications", "Stochastic Processes and Related Fields", "Ergodic Theory and Related Fields", and "Summer School on Probability Theory". Stimulated by these symposiums many interesting results were produced, which are published as the report of research results by this grant. Less
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