CO-OPERATIVE RESEARCH ON PROBABILITY THEORY

从1993年起，作为两年的项目，我们与该项目的联合研究人员和日本数学学会概率学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本的随机分析理论，我们组织了两个研讨会：维纳空间分析和随机分析。前者是伊藤康夫首创的，后者的主旋律是福岛的狄利克莱空间理论。日本在这一领域处于领先地位，许多开创性的作品都是在这些研讨会的推动下产生的。我们还与受邀的分析家和几何学家一起举办了与分析和几何有关的专题讨论会《与马尔可夫过程有关的分析》和《流形上的随机分析和大偏差理论》。在这些讨论的基础上，产生了新的研究。此外，针对…将随机分析更多地应用到物理和生物学中我们与物理学家和生物学家合作，组织了《物理与生物学中的随机分析》、《分形学及相关领域》和《无限粒子系统与流体动力学极限》三个研讨会，我们可以找到几个有趣的数学问题。随机分析在涉及控制论、金融理论等数理经济学和社会学中的数学方法的工程中已被证明是非常强大的，为此，我们组织了两个研讨会：应用领域的随机模型和随机分析的应用。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》、《随机过程及相关领域》、《遍历理论及相关领域》和《概率论暑期班》。在这些研讨会的激励下，产生了许多有趣的成果，这些成果被作为该基金的研究成果报告发表。较少

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