| Project/Area Number |
09640254
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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 | SHINSHU UNIVERSITY |
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Principal Investigator |
INOUE Kazuyuki SHINSHU UNIV., DEP.OF MATHEMATICAL SCIENCES,PROFESSOR, 理学部, 教授 (70020675)
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| Co-Investigator(Kenkyū-buntansha) |
HATTORI Kumiko SHINSHU UNIV., DEP.OF MATHEMATICAL SCIENCES,ASSOCIATE PROFESSOR, 理学部, 助教授 (80231520)
HONDA Katsuya SHINSHU UNIV., DEP.OF MATHEMATICAL SCIENCES,PROFESSOR, 理学部, 教授 (50109302)
TAKANAKA Shigeo OKAYAMA UNIV., OF SCIENCE.DEP.OF MATHEMATICS,PROFESSOR, 理学部, 教授 (80022680)
MAEJIMA Makoto KEIO UNIV., DEP.OF MATHEMATICS,PROFESSOR, 理工学部, 教授 (90051846)
玉木 大 信州大学, 理学部, 講師 (10252058)
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| Project Period (FY) |
1997 – 1998
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| Project Status |
Completed (Fiscal Year 1998)
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| Budget Amount *help |
¥3,000,000 (Direct Cost: ¥3,000,000)
Fiscal Year 1998: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 1997: ¥2,000,000 (Direct Cost: ¥2,000,000)
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| Keywords | infinitely divisible process / process with independent increments / process of Ornstein-Uhlenbeck type / dam process / Markov chain / stationary distribution |
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| Research Abstract |
We propose a stochastic model for a dam with non-additive input and investigate a Markov chain embedded in the darn content process. 'The dam process is expressed explicitly and the limiting behavior of the hidden Markov chain is considered. We are concerned with a dam process determined by piecewise linear continuous cumulative input process and release rule depending on the dam content. When the input is given by a Levy process and the release rate function is linear. we have a Markov process of Ornstein-Uhlenbeck type. This process admits a stochastic integral representation related to the Levy process and has a stationary distribution under some condition for the Levy measure. In our dam model, however, the input process is non-additive and has piecewise linear continuous sample functions. If the release rate function is either linear or quadratic, the Markov chain is described by a stochastic recurrence equation connected with random matrices, In the linear case we obtain criteria for the convergence in law and its limiting properties. In particular, a sufficient condition is given for the continuity and also the absolute continuity of the limiting distribution. Our result was presented in the Symposium on Analysis and Probability 1998. held at National Taiwan University. Taipei. November 23-27.1998.
The following paper was submitted to Trends in Probability and Related Analysis (=the Proceedings of SAP 98).
Kazuyuki INOUE and Naoki TAKAYAMA : 'A stochastic model for a dam with non-additive input'.
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