1999 Fiscal Year Final Research Report Summary
Probability Theory and Its Interface
| Project/Area Number |
09304022
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| Research Category |
Grant-in-Aid for Scientific Research (A)
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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 | KYOTO UNIVERSITY |
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Principal Investigator |
TAKAHASHI Youichiro Research Institutef for Mathematical Sciences, Kyoto University, Professor, 数理解析研究所, 教授 (20033889)
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| Co-Investigator(Kenkyū-buntansha) |
TANIGUCHI Setsuo Kyushu University, Independent Graduate School of Mathematics, Associate Professor, 大学院・数理学研究科, 助教授 (70155208)
MATSUMOTO Hiroyuki Nagoya University, School of Informatics and Sciences, Associate Professor, 情報文化部, 助教授 (00190538)
SHIGEKAWA Ichiro Graduate School of Science, Kyoto University, Professor, 大学院・理学研究科, 教授 (00127234)
KUSUOKA Shigeo The University of Tokyo, Graduate School of Mathematical Science, Professor, 大学院・数理科学研究科, 教授 (00114463)
FUNAKI Tadahisa The University of Tokyo, Graduate School of Mathematical Science, Professor, 大学院・数理科学研究科, 教授 (60112174)
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| Project Period (FY) |
1997 – 1999
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| Keywords | hydrodynamic limit / Wieener functional / Dirichlet form / large deviation and entropies / fractals / asymptotic behavior of spectrum / random walk and Brownian motion / innovation problem and noises |
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| Research Abstract |
During these three years we achieved the expected results in various areas in probability theory and contributed to promote a few new directions for the future as follows.
In stochastic analysis we have made, among others, two remarkable progresses. One is the study of inequalities and their role in the analysis of function spaces on infinite dimensional, Wiener space led by Aida and Shigekawa. The other is the study of asymptotic behaviors for the Wiener functionals of exponential type by Taniguchi, Matsumoto et al. Besides them, we should mention on the trend to generalize the stochastic analysis based on the Dirichlet space theory shown, for instance, in the work of Osada.
In the theory of hydrodynamic limit Funaki, Uchiyama and thier pupil attacked more realistic models successfully and reached to the promissing problem to compare and synthesize their results with the results obtained in the Dirichlet space theory mentioned above.
In ergodic theory and its around the most remarkable progress was made in the study of the decay of correlation functions by Morita. The summer school in 1997 in this area influenced the information theory people and Han made a large deviation theory for coding.
The renewal of the classical theories and techniques was one of the slogans of the project, which was also successful as is shown by Kumagai on analysis on fractals, Atsuji on Nevalinna theory, Hamana on random walk functionals and Shirai et al. on the spetrum of graph.
Moreover, Nagai et al. applied stochastic control techniques to mathematical finance and Sugita, Takanobu et al. contributed to quasi-random nember theory by using Weyltransformation.
We owed much to PE S. Watanabe to have organized a summer school in 1999 on the noise problem. Also we owed much to the modification on the international exchange under the grant-in-aids by JSPS which has brought more fruitful results.
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