Integrated Research on Equilibrium Random Phenomena

平衡随机现象的综合研究

基本信息

批准号：
10304006
负责人：
KUBO Izumi
金额：
$ 14.02万
依托单位：
Hiroshima University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (A).
财政年份：
1998
资助国家：
日本
起止时间：
1998 至 2000
项目状态：
已结题

项目摘要

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 … More 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

各种重要的随机现象被认为是等效状态。从这个角度来看，我们已经研究了三年。在此期间，我们举行了赠款的24次研讨会。这里沿着下面的关键单词描述了我们的一些结果。1随机分析：艾达在循环空间上取得了非常深刻的结果，尤其是关于log-sobolev的不平等，光谱差距，克拉克蛋白配方奶粉等。2非线性和随机分析：Funaki在汉堡方程式上进行了研究，研究了汉堡方程，尤其是针对整体效果的潮流，尤其是对全球性的解决方案，其范围的潮流，该潮流的存在等，其范围的潮流，既定的，又是全球性的，曾经是繁琐的，又是繁琐的。解决方案。3白噪声分析：Kubo给出了一种新的白噪声空间构造方法，这是非常清晰和一般的。他也给出了良好的描述定理。这些结果在加尔各答的印度统计研究所举行的研讨会上提出。奥巴塔通过……更多符号研究了操作员在空间上的表征。他应用了随机微分方程。4信息分析：Ihara用反馈进行了非常通用的高斯通道，并证明了共同信息的一般公式。他讨论了大型出发理论对信息理论的应用。在固定高斯源的情况下，UE获得了误差的最小编码率。奥卡贝（Okabe）开发了一个集成的系统，该系统由他提出的各种测试，以根据“波动和偏差定理”的原则分析时间序列。此外，他为度量向量中的流量构建了km_20-langevin方程。 Maejima介绍了半自我相似分布的概念，并将其扩展到了半自我相似的过程，操作员半自我相似的分布等。他对它们进行了非常深入的研究。在报告和共同研究人员的列表中，发现了其他结果。较少的