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Parabolic potential theory and Markov processes; basic theory and its applications

Research Project

Project/Area Number 03640221
Research Category

Grant-in-Aid for General Scientific Research (C)

Allocation TypeSingle-year Grants
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionKumamoto University

Principal Investigator

OSHIMA Yoichi  Kumamoto Univ.,Eng.,Professor, 工学部, 教授 (20040404)

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)
Project Period (FY) 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)
KeywordsDirichlet forms / Parabolic potentials / space-time processes / Schrodinger processes / 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 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.

Report

(3 results)
  • 1992 Annual Research Report   Final Research Report Summary
  • 1991 Annual Research Report
  • Research Products

    (53 results)

All Other

All Publications (53 results)

  • [Publications] Y.Oshima: "On conservativeness and recurrence criteria for Markov processes" Potential Analysis. 1. 115-131 (1992)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] Y.Oshima: "On a construction of Markov processes associated with time dependent Dirichlet spaces" Forum Math. 4. 395-415 (1992)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] Y.Oshima: "Some properties of Markov processes associated with time dependent Dirichlet forms" Osaka J.Math.29. 103-127 (1992)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] M.Hitsuda: "Canonical representations of Gaussian processes and integral operators" Proceedings of the third Nagoya Levy Seminar. 214-226 (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] Takao Nambu: "Stabilization of parabolic systems via a degenerate nonnegative feedback" J.Dynamics and Differential Equations. 3. 399-422 (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] Takao Nambu: "Continuous dependence of solutions to the Lyapunov equation relative to an elliptic differential operator of order 2" Math.Control Signals and Systems. 5. 195-216 (1992)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] T.Nambu: "Robustness of a feedback control scheme for one-dimensional diffusion equations:Perturbation to the Sturm-Liouville operator" Proc.Roy.Soc.Edinburgh. 121A. 349-359 (1992)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] T.Nambu: "Robustness of feedback control systems of parabolic type against perturbations to an elliptic operator" J.Differential Equations.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] T.Nambu: "On the Equation Describing the Random Motim of Mutnally Reflecting Molecules" Japan Academy. 67. 293-298 (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] Y.Saisho: "A Brownian ball iteracting with infinitely many Brownian particles in R^d" Tokyo J.Math.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] Y.Saisho and H.Tanemura: "The heteroscedastic method II:Simplified sampling" Amer.J.Math.Manage.Sci.11. 263-276 (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] E.J.Dudewicz,H.Hyakutake and V.S.Taneja: "Selecting the better component of a bivariate exponential distribution" Statist.Decisions. 10. 153-162 (1992)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] H.Hyakutake: "Note on selecting the better component of the bivariate exponential distribution" Hiroshima Math.J.23.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] H.Hyakutake: "On a general selection procedure for multivariate normal populations:Asymptotic approximation to constants" Amer.J.Math.Manage.Sci.13.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] 坂田 年男・高田 佳和・百武 弘登: "基礎統計学,朝倉出版" 朝倉出版, 157 (1992)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] M.Fukushima,Y.Oshima,M.Takeda: "Dirichlet Forms and Symmetric Markov Processes" Walter de Gruyter & Co., 300 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] Y.Oshima: "On conservativeness and recurrence criteria for Markov processes" Potential Analysis. Vol.1. 115-131 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] Y.Oshima: "On a construction of Markov processes associated with time dependent Dirichlet spaces" Forum Math.Vol.4. 395-415 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] Y.Oshima: "Some properties of Markov processes associated with time dependent Dirichlet forms" Osaka J. Math.Vol.29. 103-127 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] M. Hitsuda: "Canonical representations of Gaussian processes and integral operators, Gaussian random fields" Proceedings of the third Nagoya Levy Seminar. 214-226 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] T.Nambu: "Stabilization of parabolic systems via a de-generate nonnegative feedback" J. Dynamics and Differential Equations. Vol.3 No.3. 399-422 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] T.Nambu: "Continuous dependence of solutions to the Lyapunov equation relative to an elliptic differential operator of order 2" Math. Control Signals and Systems. Vol.5,No.2. 195-216 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] T. Nambu: "Robustness of a feedback control scheme for one-dimensional diffusion equations: Perturbation to the Sturm-Liouville operator" Proc. Roy. Soc. Edinburgh, Sec. A. Vol.121A, parts 3/4. 349-359 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] T.Nambu: "Robustness of feedback control systems of parabolic type against perturbations to an elliptic operator" J. Differential Equations.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] T.Saisho: "On the Equation Describing the Random Motim of Mutnally Reflecting Molecules" Japan Academy. Vol.67,Ser.A. 293-298 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] Y.Saisho and H.Tanemura: "A Brownian ball interacting with infinitely many Brownian particles in R^d" Tokyo J.Math.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] E.J.Dudewicz, H.Hyakutake and V.S.Taneja: "The heteroscedastic method II: simplified sampling" Amer. J. Math. Manage. Sci.Vol.11. 263-276 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] H.Hyakutake: "Selecting the better component of a bi-variate exponential distribution" Statist. Decisions. Vol.10. 153-162 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] Hiroto Hyakutake: "Note on selecting the better component of the bivariate exponential distribution" Hiroshima Math.J.Vol.23.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] H.Hyakutake: "On a general selection procedure for multivariate normal populations: Asymptotic approximation to constants" Amer.J.Math.Manage.Sci.Vol.13.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] Y.Oshima: "On conservativeness and recurrence criteria for Markov processes" Potential Analysis. 1. 115-131 (1992)

    • Related Report
      1992 Annual Research Report
  • [Publications] Y.Oshima: "On a construction of Markov processes associated with time dependent Dirichlet spaces" Forum Math.4. 395-415 (1992)

    • Related Report
      1992 Annual Research Report
  • [Publications] Y.Oshima: "Some properties of Markov processes associated with time dependent Dirichlet forms" Osaka J.Math.29. 103-127 (1992)

    • Related Report
      1992 Annual Research Report
  • [Publications] T.Nambu: "Continuous dependence of solutions to the Lyapunov equation relative an elliptic differential operator of order 2" Math.Control Signals and Systems. 5. 195-216 (1992)

    • Related Report
      1992 Annual Research Report
  • [Publications] T.Nambu: "Robustness of a feedback control scheme for one-dimensional diffusion equations:Perturbation to the Sturm-Liouville operator" Proc.Roy.Soc.Edinburgh. 121A. 349-359 (1992)

    • Related Report
      1992 Annual Research Report
  • [Publications] T.Nambu: "Robustness of feedback control systems of parabolic type against perturbations to an elliptic operator" J.Differential Equations.

    • Related Report
      1992 Annual Research Report
  • [Publications] Y.Saisho and H.Tanemura: "A Brownian ball iteracting with infinitely many Brownian particles in R^d" Tokyo J.Math.

    • Related Report
      1992 Annual Research Report
  • [Publications] H.Hyakutake: "Selecting the better component of a bivariate exponential distribution,Statist.Decisions" Statist.Decisions. 10. 153-162 (1992)

    • Related Report
      1992 Annual Research Report
  • [Publications] H.Hyakutake: "Note on selecting the better component of the bivariate exponential distribution" Hiroshima Math.J.23.

    • Related Report
      1992 Annual Research Report
  • [Publications] H.Hyakutake: "On a general selection procedure for multivariate normal populations:Asymptotic approximation to constants" Amer.J.Math.Manage.Sci.13.

    • Related Report
      1992 Annual Research Report
  • [Publications] 坂田 年男・高田 佳和・百武 弘登: "基礎統計学" 朝倉出版, 157 (1992)

    • Related Report
      1992 Annual Research Report
  • [Publications] M.Fukushima,Y.Oshima,M.Takeda: "Dirichlet Forms and Symmetric Markov Processes" Walter de Gruyter & Co., 300 (1993)

    • Related Report
      1992 Annual Research Report
  • [Publications] Y.Oshima: "On conservativeness and recurrence criteria for Markov processes" Potential Analysis. (1992)

    • Related Report
      1991 Annual Research Report
  • [Publications] Y.Oshima: "On a construction of Markov processes associated with time dependent Dirichlet spaces" Forum.Math.(1992)

    • Related Report
      1991 Annual Research Report
  • [Publications] Y.Oshima: "Some properties of Markov processes associated with time dependent Dirichlet ferms" Osaka J.Math.29. (1992)

    • Related Report
      1991 Annual Research Report
  • [Publications] M.Hitsuda: "Canonical representations of Gaussian processes and integral operators" Gaussian random fields,Proceedings of the third Nagoya Levy Seminar. 214-226 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] Takao Nambu: "Continuous dependence of solutions to the Lyapunov equation relative to an elliptic differential operator of order 2" Math.Control,Signals,and Systems. 5. (1992)

    • Related Report
      1991 Annual Research Report
  • [Publications] Takao Nambu: "Robusthess of a feedback control scheme for oneーdimensional diffusion equations:perturbation to the SturmーLiouville operator" Proc.Roy.Soc.Edinburgh,Sec.A. 120A. (1992)

    • Related Report
      1991 Annual Research Report
  • [Publications] Takao Nambu: "Stabilization of parabolic systems via a degenerate nonnegative feedback" J.Dynamics and Differential Equations. 3. 399-422 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] Yasumasa Saisho: "On the Equation Describing the Random Notion of Mutually Reflecting Molecules" Proc.Japan Acad.Ser.A. 67. 293-298 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] Edward J.Dudewicz Hiroto Hyakutake Vidya S.Taneja: "The Heteroscedastic Method II:Simplified Sampling" Amer.J.Math.Manage.Sci.11. (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] Hiroto Hyakutake: "Selecting the better component of a bivariate exponential distribution" Statistics & Decisions. 10. (1992)

    • Related Report
      1991 Annual Research Report
  • [Publications] 坂田 年男,高田 佳和,百武 弘登: "基礎統計学" 朝倉書店, 160 (1992)

    • Related Report
      1991 Annual Research Report

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Published: 1991-04-01   Modified: 2016-04-21  

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