2000 Fiscal Year Final Research Report Summary
Stochastic analysis and stochastic control for symmetric Markov processes
| Project/Area Number |
11640142
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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 | KANSAI UNIVERSITY |
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Principal Investigator |
FUKUSHIMA Masatoshi Kansai Univ., Faculty of Engineering, Prof., 工学部, 教授 (90015503)
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| Co-Investigator(Kenkyū-buntansha) |
YAMAMOTO Noboru Kansai Univ. Faculty of Engineering. Prof., 工学部, 教授 (80029628)
ISII Keiiti Kansai Univ. Faculty of Engineering, Prof., 工学部, 教授 (80029420)
KURISU Tadashi Kansai Univ. Faculty of Engineering, Prof., 工学部, 教授 (00029159)
MAEDA Toru Kansai Univ. Faculty of Engineering, Associate Prof., 工学部, 助教授 (20199623)
HIRASHIMA Yasumasa Kansai Univ. Faculty of Engineering. Associate Prof., 工学部, 助教授 (80047399)
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| Project Period (FY) |
1999 – 2000
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| Keywords | symmetic Markov processes / Dirichlet forms / stochastic analysis / stochastic control / semi-martingale / Ito's formula / BV functions / stochastic games |
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| Research Abstract |
For a general symmetric Markov process X(t) and a function u in the associated quasi-regular Dirichlet space, the head investigator succeeded to give a quite useful necessary and sufficient conditions for the composite process u(X(t)) to be a semimartingale.
Then he cooperates with other investigators to apply the above mentioned general criteria first for symmetric diffusion processes in finite dimensions to identify necessary and sufficient smoothness for a function to make Ito's formula invariant. Second, finite dimensional notions of BV functions are extended to the infinite dimensional abstract Wiener space and the associated Gauss formula and the Skorohod 1 equations are exploited. The head investigator also has written a joint paper on a singular control problem with Professor Taksar by extending a previous paper by Taksar considerably, combining it with a Nagai-Zabczyk characterization of a stochastic zero sum game by a Dirichelt form.
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