1993 Fiscal Year Final Research Report Summary
Research on Probability Theory and Related Problems of Analysis
| Project/Area Number |
04452011
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| Research Category |
Grant-in-Aid for General Scientific Research (B)
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| Allocation Type | Single-year Grants |
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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) |
MAEDA Yoshiaki Keio Univ., Sci.& Tech., Associate Professor, 理工学部, 助教授 (40101076)
SHIOKAWA Ietaka Keio Univ., Sci.& Tech., Professor, 理工学部, 教授 (00015835)
KIKUCHI Norio Keio Univ., Sci.& Tech., Professor, 理工学部, 教授 (80090041)
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) |
1992 – 1993
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| Keywords | Diffusion Process / Brownian Motion / Random Environment / Operator-stable Process / Ergodic Transformation of Type II*& III / Harmonic Map / Morse-flow / Infinite Dimensional Lie Algebra |
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| Research Abstract |
1.Problems for random environments and self-similar processes. Results concerning localization by random centering were obtained for a diffusion process in a Brownian environment or more generally for a diffusion process in a random environment belonging to a considerably wider class of asymptotically self-similar random walks. To extend these results to the case the environment is a levy process H.Tanaka obtained some new results for superharmonic transforms of absorbing Levy processes. It was aoso proved that a diffusion process in a multidimensional Brownian environment is recurrent. As for self-simitar processes M.Maejima investigated operator-stabel processes and obtained new results, in particular, for their fundamental properties, examples and related limit theorems.
2.In ergodic theory characteristic properties of ergodic transformations without finite invariant measures were ingestigated and new results were obtained concerning the role of asymptotic property of the associated cocycles in the classification problem.
3.N.Kikuchi contructed Morse-flows associated with certain variational problems.
4.In an analytic-numbertheoretic approach to disordered systems I.Shiokawa obtained new resuts for complexity of certain sequences arising in a billiard problem.
5.An extension of Poincare-Birkoff-Witt theorem to infinite dimensional Lie algebras was gigen.
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