Grant-in-Aid for Scientific Research (A).
General mathematics (including Probability theory/Statistical mathematics)
|Research Institution||Hiroshima University|
KUBO Izumi Hiroshima Univ.Graduate School of Sci., Prof., 大学院・理学研究科, 教授 (70022621)
MAEJIMA Makoto Keio Univ., Faculty of Science and Technology, Prof., 理工学部, 教授 (90051846)
井原 俊輔 名古屋大学, 情報文化学部, 教授 (00023200)
FUNAKI Tadahisa Univ.of Tokyo, Graduate School of Mathematical Science, Prof., 大学院・数理科学研究科, 教授 (60112174)
平良 和昭 筑波大学, 数学系, 教授 (90016163)
岩田 耕一郎 広島大学, 理学部, 助教授 (20241292)
佐藤 坦 九州大学, 大学院・数理学研究科, 教授 (30037254)
OKABE Yasunori Univ.of Tokyo, Graduate School of Engineering, Prof., 大学院・工学研究科, 教授 (30028211)
AIDA Shigeki Osaka Univ., Graduate School of Engineering Science, Assoc.Prof., 大学院・基礎工学研究科, 助教授 (90222455)
OBATA Nobuaki Nagoya Univ., Graduate School of Mathematics, Assoc.Prof., 大学院・多元数理科学研究科, 助教授 (10169360)
|Project Fiscal Year
1998 – 2000
Completed(Fiscal Year 2000)
|Budget Amount *help
¥21,900,000 (Direct Cost : ¥21,900,000)
Fiscal Year 2000 : ¥7,400,000 (Direct Cost : ¥7,400,000)
Fiscal Year 1999 : ¥7,000,000 (Direct Cost : ¥7,000,000)
Fiscal Year 1998 : ¥7,500,000 (Direct Cost : ¥7,500,000)
|Keywords||Stochastic Analysis / Infinite dimensional Analysis / White Noise Analysis / Informatic Analysis / Non-Linear Analysis / Quantum Analysis / Dynamical Systems / Self-Similar Processes / 確率解析 / 無限次元解析 / 白色雑音解析 / 情報解析 / 非線形解析 / 量子解析 / 力学系 / 自己相似過程 / 確率論 / 平衡現象 / 複雑系 / フラクタル / エルゴード理論 / 情報理論 / ガウス過程 / 安定過程|
Various important random phenomena are considered as equilibrium states. In this point of view, we have researched for three years. In the period, we held 24 symposia by the grant. Here some of our results are described along key words below.
1 Stochastic Analysis : Aida got very deep results on loop spaces especially about log-Sobolev inequalities, spectral gaps, Clark-Ocone formula etc.
2 Non-Linear and Stochastic Analysis : Funaki researched on Burger equations with fractal Laplacian, especially about the existence of global solution, the uniqueness, the regularities etc. Further, he researched progressive wave solutions and self-similar solutions.
3 White Noise Analysis : Kubo gave a new method of construction of white noise spaces, which is very clear and general. He gave also good characterization theorems. Those results were presented in the symposium held at Indian Statistical Institute in Calcutta. Obata researched the characterization of operators on the spaces by means of their
symbols. He applied it stochastic differential equations.
4 Informatic Analysis : Ihara researched very general Gaussian channels with feed back and proved a general formula of mutual information. He discussed applications of large deviation theory to information theory. ue obtained the minimum coding rate for error in the case of stationary Gaussian source. Okabe developed an integrated system of various tests which had been proposed by him to analyze time series under the principle of "Fluctuation and Deviation Theorem". Further he constructed KM_20-Langevin equation for flow in metric vectors and applied it.
5 Self Similar Process : Takenaka showed the deterministic property of distribution of SaS-processes by its finite dimensional distributions. Maejima introduced the concept of semi-self-similar distributions and extended it to that of semi-self-similar processes, operator semi-self-similar distributions and etc. He researched them very deeply.
Other results are found in the report and lists of papers by co-researchers. Less