1991 Fiscal Year Final Research Report Summary
An approach to the control theory by analytic and geometric methods.
| Project/Area Number |
02640192
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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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 | Waseda Univ. |
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Principal Investigator |
ISHIGAKI Haruo Waseda Univ. School of Education Professor, 教育学部, 教授 (60063492)
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| Co-Investigator(Kenkyū-buntansha) |
KAKITA Takao Waseda Univ., School of Science and Engineering, Professor, 理工学部, 教授 (90063362)
SUNOUCHI Haruo Waseda Univ. School of Science and Engineering, Professor, 理工学部, 教授 (80063238)
SUZUKI Shin'ichi Waseda Univ., School of Education Professor, 教育学部, 教授 (10030777)
MIYADERA Isao Waseda Univ., School of Education Professor, 教育学部, 教授 (50063293)
WADA Junzo Waseda Univ., School of Education Professor, 教育学部, 教授 (50063342)
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| Project Period (FY) |
1990 – 1991
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| Keywords | Control Theory / Random Process / Portofolio / Stochastic differential Equation / Semigroup Theory / cox'sモデル |
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| Research Abstract |
There are many control problems of the systems described as a random process. For example, H-J-B equation was derived from optimal control problems subject to the stochastic differential equation. These equations have viscosity solutions but non usual solution.
We have tried to obtain a semigroup solution and to characterize the optimal control. For very special case, a kind of portfolio problem, we could express the solution in direct form, and get a criterion of optimality.
The other hand, We have tried to extend the semigroup theory, and obtained some results about the C-semigroup.
Another our results are about the space of continuous functions as the space of sample pathes. As a gcometric approach, We have studied the graph theory.
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