Research on Probability and Related Topics of Analysis

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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.