| Project/Area Number |
03640221
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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 | Kumamoto University |
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Principal Investigator |
OSHIMA Yoichi Kumamoto Univ.,Eng.,Professor, 工学部, 教授 (20040404)
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| Co-Investigator(Kenkyū-buntansha) |
YOKOI Yoshitaka Kumamoto Univ.,Gen. Ed.,Associate Prof., 教養部, 助教授 (50040481)
HYAKUTAKE Hiroto Kumamoto Univ.,Eng.,Lecturer, 工学部, 講師 (70181120)
SAISHO Yaumasa Kumamoto Univ.,Eng.,Associate Prof., 工学部, 助教授 (70195973)
HITSUDA Masuyuki Kumamoto Univ.Sci.,Professor, 理学部, 教授 (50024237)
NAMBU Takao Kumamoto Univ.,Eng.,Professor, 工学部, 教授 (40156013)
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| Project Period (FY) |
1991 – 1992
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| Keywords | Dirichlet forms / Parabolic potentials / space-time processes / Schrodinger processes |
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| Research Abstract |
The purpose of this research is to extend the correspondence between Dirichlet forms and Markov processes to a class including space-time Markov processes. Since the generator of the space time process degenerate to the time direction, it is out of the framework of the standard theory of Dirichlet forms. Instead, we consider a time dependent family of Dirichlet forms and construct an associated space-time process. This became possible by formulating the results of parabolic potential theory in the form suitable for our present purpose. We next studied the correspondence of various notions between time dependent Dirichlet forms and Space-time processes such as; capacity, equilibrium potential, locality and continuity,..., and showed that mast of the Dirichlet forms are possible. As an application of this result, we gave a construction and conservativeness of Schrodinger processes which is given by a singular local martingale transformation of non-homogeneous Markov processes. We also made a progre on the researches of standard or non-standard representation of Gaussian processes, interacting systems of infinitely many Brownian balls, stability and controllability of parabolic control systems and estimation theory of multivariate distributions.
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