CO-OPERATIVE RESEARCH ON PROBABILITY THEORY

从1993年开始，我们与该项目的联合研究人员和日本数学学会概率部分的其他研究人员合作，进行了为期两年的“概率论及相关主题”的合作研究。首先，针对现代概率论中最基本的随机分析理论的进一步发展，我们组织了“维纳空间分析”和“随机分析”两个专题讨论会。前者是由伊藤启一和后者的一个主要主题是狄利克雷空间理论由于M.在这一领域，日本是领先的国家，许多开创性的工作是在这些研讨会的推动下产生的。我们还与受邀的分析师和几何学家共同举办了与分析和几何相关的研讨会“与马尔可夫过程相关的分析”和“流形上的随机分析和大偏差理论”。在此基础上进行了新的研究。此外，针对 ...更多信息 随机分析在物理学和生物学中的应用我们与物理学家和生物学家合作组织了“物理学和生物学中的随机分析”、“分形及相关领域”和“无限粒子系统和流体动力学极限”三个专题讨论会，从中我们可以发现一些有趣的数学问题。随机分析在控制理论、金融理论等数理经济学和社会学中的数学方法等工程领域中的应用已被证明是非常强大的，为此我们组织了“随机模型在应用领域中的应用”和“随机分析的应用”两次研讨会。此外，为了讨论概率论杂项问题的新结果，我们组织了“高斯和稳定过程及其应用”，“随机过程和相关领域”，“遍历理论和相关领域”和“概率论暑期学校”。在这些研讨会的激励下，产生了许多有趣的结果，这些结果作为该基金的研究成果报告发表。少

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 … More 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