1998 Fiscal Year Final Research Report Summary
Asymptotic Analysis of Probability Laws and Path Behaviors for Markov Processes
| Project/Area Number |
09640293
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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 | Faculty of Science, Toho University |
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Principal Investigator |
SHIMURA Michio Toho Univ., Fac.of Science, Professor, 理学部, 教授 (90015868)
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| Co-Investigator(Kenkyū-buntansha) |
KOTANI Motoko Toho Univ., Fac.of Science, Associate Prof., 理学部, 助教授 (50230024)
OHGUCHI Takeshi Toho Univ., Fac.of Science, Associate Prof., 理学部, 助教授 (60168888)
TANEMURA Hideki Chiba Univ., Fac.of Science, Associate Prof., 理学部, 助教授 (40217162)
NISHIOKA Kunio Toho Univ., Fac.of Science, Associate Prof., 理学部, 助教授 (60101078)
TSUKADA Makoto Tokyo Metro.Univ., Fac.of Science, Professor, 理学部, 教授 (10120198)
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| Project Period (FY) |
1997 – 1998
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| Keywords | random walk / infinite particle system / stochastic numerical analysis / Laplacian on a graph / harmonic map / spectral structure / biharmonic operator / operator algebra |
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| Research Abstract |
In this reseach project, Shimura considered asymptotic analysis for the exit probability of two dimensional random walk with drift from a quadrant, applying a technique from Monte Carlo Method. He examined applicability of some consequence from the theory of random walk defined on a Markov chain to the problem. Nishioka obtained "Ito calculus" and "Girsanov formula" for the biharmonic psudo process with the biharmnic operator as its generator. He also investigated some properties of solutions for a class of quasilinear biharmonic equations which is related with some problem from the fluid dynamics. Tanemuira considered precisely the uniqueness and the ergodicity for the infinite Brownian particle system with a hard core potential. Kotani obtained an asymptotic formula for the transition probability of a random walk on some infinite graphs. She also considered the spectral structure of some harmonic maps. Tsukada investigated the sufficiency for the statistics of some stochastic processes and infinite particle systems from the point of operator algebra. Ohguchi dealt with the numerical analysis of some Markov chains related to the finance, in which he examined usefulness of some quasi-random numbers.
During the term of this project, the project members exchanged the related rescent results with M.Kondo (Shimane Univ.), K.Hirano (Osaka Univ.), T.Watanabe. (Okayama Science Univ.), M.Motoo (Tokyo Institute Technology), T.Yamada (Ritsumekan Univ.) and S.Sato (Tokyo Denki Univ.).
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