Project/Area Number  03640221 
Research Category 
GrantinAid for Scientific Research (C).

Research Field 
General mathematics (including Probability theory/Statistical mathematics)

Research Institution  Kumamoto University 
Principal Investigator 
OSHIMA Yoichi Kumamoto Univ.,Eng.,Professor, 工学部, 教授 (20040404)

CoInvestigator(Kenkyūbuntansha) 
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)

Project Fiscal Year 
1991 – 1992

Project Status 
Completed(Fiscal Year 1992)

Budget Amount *help 
¥1,800,000 (Direct Cost : ¥1,800,000)
Fiscal Year 1992 : ¥800,000 (Direct Cost : ¥800,000)
Fiscal Year 1991 : ¥1,000,000 (Direct Cost : ¥1,000,000)

Keywords  Dirichlet forms / Parabolic potentials / spacetime processes / Schrodinger processes / ディリクレー形式 / 放物型ポテンシャル / 時空過程 / シュレージンガー過程 / ディリクレ形式 / シュレジンガ過程 / Parabolic Potential / Diriソhlet spaces / Hunt process 
Research Abstract 
The purpose of this research is to extend the correspondence between Dirichlet forms and Markov processes to a class including spacetime 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 spacetime 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 Spacetime 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 nonhomogeneous Markov processes. We also made a progre on the researches of standard or nonstandard representation of Gaussian processes, interacting systems of infinitely many Brownian balls, stability and controllability of parabolic control systems and estimation theory of multivariate distributions.
