Research on Probability and Related Topics of Analysis

1. (1)H.Tanaka对白色噪声环境中具有常数正漂移系数kappa的布朗运动（扩散过程）的长时间渐近行为给出了新的结果，其结果随kappa的变化而变化. (2)在算子自相似过程的极限定理（M.Maejima），非对称马氏过程的大偏差问题，Z上某自旋系统的构造和流体动力学极限（Y.Suzuki）等方面获得了新的结果.伊藤澄清了一些数论结构的“无限集的整数”出现作为一个不变的分类遍历变换没有有限不变的措施，特别是，类型II_* 和III.3。金井先生在研究群体行为时提出了一种基于随机分析的新方法。Y.Maeda研究了引入相关zeta函数的某些群的自同态。关于不可压Navier-Stokes方程局部解和整体解的一些新结果（A.Tani）. I.Shiokawa（和其他人）研究了某些与Jacobi的θ级数或Fibonacci序列有关的数的超越性问题，解决了Liouville（1851）关于超越数的猜想。

1. (1) New results for long time asymptotic behavior of a Brownian motion (diffusion process) with a constant positive drift coefficient kappa in a white noise environment Were obtained by H.Tanaka ; the results vary with kappa. (2) New results were obtained (i) in the limit theorem of operator-self-similar processes (by M.Maejima), (ii) in a problem of large deviation of Nonsymmetric Markov processes and (iii) for the construction and hydrodynamic limit of a certain spin system on Z (by Y.Suzuki).2. Y.Ito clarified some number-theoretic structure of "infinite sets of integers" arising as an invariant in the classification of ergodic transformations without finite invariant measures, in particular, of the types II_* and III.3. A new approach based on stochastic analysis was poposed by M.Kanai in the investigation of group actions. Y.Maeda investigated certain groups of diffeomorphisms introducing the associated zeta functions.4. Some new results concerning local and global solutions of the incompressible Navier-Stokes equations (by A.Tani).5. I.Shiokawa (and others) investigated the transcendentality problem of certain numbers connected with Jacobi's theta series or with Fibonacci sequences, solving a conjecture by Liouville (1851) on transcendental numbers.