1999 Fiscal Year Final Research Report Summary
Laplace approximations and related limit theorems
| Project/Area Number |
10640134
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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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 |
TAMURA Yozo Keio Univ., Fac. Sci. and Tech., Prof., 理工学部, 助教授 (50171905)
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| Co-Investigator(Kenkyū-buntansha) |
TANAKA Hiroshi Japan Women's Univ., Fac. Sci., Prof., 理学部, 教授 (70011468)
SUZUKI Yuki Keio Univ., Fac. Sci. and Tech., Instr., 理工学部, 助手 (30286645)
MAEJIMA Makoto Keio Univ., Fac. Sci. and Tech., Prof., 理工学部, 教授 (90051846)
TANEMURA Hideki Chiba Univ., Fac. Sci., Ass. Prof., 理学部, 助教授 (40217162)
CHIYONOBU Taizo Nagoya Univ., Grad. Sch. Math., Instr., 大学院・多元数理科学, 助手 (50197638)
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| Project Period (FY) |
1998 – 1999
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| Keywords | large deviation / Laplace approximation / random environment |
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| Research Abstract |
1. On the problem for Laplace approximateion for large deviation principle first of all, we got a general framework of the precise estimate of the usual Laplace approximation order for non-symmetric Markovian processes in the case that the Hessian of the free energy functional may be degenerate. Secondly, for the non-usual order problem of Laplace approximations for large deviation principle, the new type of limit theorem was obtained by mainly Prof. T. Chiyonobu in the case of I.I.d. random variables under suitable conditions motivated by the limit theorems of random matrices.
2. On the problems for the distributions of stochastic processes in random environments, firstly, mainly Profs. H. Tanaka and Y. Suzuki got the new type of limit theorem for one-dimensional diffusion processes with one- sided Brownian potential. Secondly a homogenization result was obtained for a random walk on some kind of fraktals with H. Takahashi related to some results for critical phenomena. On the other hand, on the problem of infinitely many balls reflecting mutually and with suitable potentials, mainly Prof. H. Tanemura constructed such infinitely many balls system through SDE method.
3. On the problems for self similar processes, we got some result for multidimensional infinitely divisible distributions and their projections with Prof. M. Maejima. We also introduced the operator semi-selfsimilar processes and got some basic properties with Prof. M. Maejima and T. Saigo.
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