CO-OPERATIVE RESEARCH ON PROBABILITY THEORY

作为1993年开始的两年项目，我们与该项目的联合研究人员和日本数学会概率论部的其他研究人员合作开展了“概率论及相关课题”的合作研究。首先，为了进一步发展现代概率论中最基础的随机分析理论，我们组织了“维纳空间分析”和“随机分析”两场专题讨论会。前者是由伊藤k .发起的，后者则是由福岛m .提出的狄利克雷空间理论。在这一领域，日本是领先的国家，许多开创性的作品都是在这些研讨会的推动下产生的。我们还与特邀分析师和几何学者共同举办了与分析和几何相关的“与马尔可夫过程相关的分析”和“流形的随机分析与大偏差理论”研讨会。在讨论的基础上，产生了新的研究。此外，为了将随机分析更多地应用于物理和生物学，我们与物理学家和生物学家合作举办了“物理和生物学中的随机分析”、“分形及其相关领域”和“无限粒子系统与流体动力极限”三场研讨会，并发现了一些有趣的数学问题。事实证明，随机分析在涉及控制理论、金融理论等数学经济学和社会学中的数学方法的工程中是非常强大的，为此我们组织了“应用领域中的随机模型”和“随机分析的应用”两场研讨会。此外，为了讨论概率论中各种问题的新结果，我们组织了“高斯与稳定过程及其应用”、“随机过程及其相关领域”、“遍历理论及其相关领域”和“概率论暑期学校”。在这些研讨会的刺激下，产生了许多有趣的结果，这些结果作为研究结果报告发表。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