| Project/Area Number |
07454034
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Keio University |
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Principal Investigator |
TANAKA Hiroshi Keio Univ., Sci.& Tech., Professor, 理工学部, 教授 (70011468)
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| Co-Investigator(Kenkyū-buntansha) |
KANAI Masahiko Keio Univ., Sci.& Tech., Associate Professor, 理工学部, 助教授 (70183035)
SHIOKAWA Ietaka Keio Univ., Sci.& Tech., Professor, 理工学部, 教授 (00015835)
MAEDA Yoshiaki Keio Univ., Sci.& Tech., Professor, 理工学部, 教授 (40101076)
ITO Yuji Keio Univ., Sci.& Tech., Professor, 理工学部, 教授 (90112987)
MAEJIMA Makoto Keio Univ., Sci.& Tech., Professor, 理工学部, 教授 (90051846)
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| Project Period (FY) |
1995 – 1996
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| Keywords | Brownian Motion / Diffusion Process / Operator-Self-Similar Process / Limit Theorem / Rigidity of Group Actions / Transcendental Number / Ergodic Transformation / Large Deviation |
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| Research Abstract |
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.
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