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Separation and Fusion of Information in Stochastic Processes.

Research Project

Project/Area Number 01540190
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

HITSUDA Masuyuki  Kumamoto University Fac. Sci. Professor, 理学部, 教授 (50024237)

Co-Investigator(Kenkyū-buntansha) SAISHO Yasumasa  Kumamoto University Fac. Eng., Lecturer., 工学部, 講師 (70195973)
OKA Yukimasa  Kumamoto University Fac. Sci., Ass, Professor, 理学部, 助教授 (50089140)
OSHIMA Yoichi  Kumamoto University Fac. Eng. Professor, 工学部, 教授 (20040404)
吉田 清  熊本大学, 理学部, 助教授 (80033893)
Project Period (FY) 1989 – 1990
Project Status Completed (Fiscal Year 1990)
Budget Amount *help
¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 1990: ¥1,000,000 (Direct Cost: ¥1,000,000)
KeywordsGaussian process / Brownian motion / Canonical representation / filtering / innovation / stochastic integral / stochastic equation. / 新生過程 / 再生核ヒルベルト空間 / マルチンゲ-ル / 多重マルコフ過程
Research Abstract

Stochastic processes, especially Gaussian processes, increase their own information as time-parameter is increasing. The fact is described in terms of the increasing systems of sigma-fields generated by the "past" of the processes. It is generally difficult to find out the structure of the increasing system of the sigma-fields. In the theory of Gaussian processes, the structures are considered by P. Levy, T. Hida and many authors. The so-called Levy-Hida canonical representation makes it possible to find out the innovation from a given Gaussian process. In other words, we can find how many independent increments processes are included in the Gaussian process. In the present investigation, a Gaussian semimartingale is considered from the view point of the "innovation problems". The main results are (1) establishment of necessary an d sufficient condition for a Gaussian semimartingale to have the single innovation (equivalently to have multiplicity one), and (2) an extension of the innovation theorem due to Shiryaev and Kailath. The second result is well applicable to the theory of canonical representation.

Report

(3 results)
  • 1990 Annual Research Report   Final Research Report Summary
  • 1989 Annual Research Report
  • Research Products

    (24 results)

All Other

All Publications (24 results)

  • [Publications] Masuyuki Hitsuda: "Canonical representation of Gaussian semimatingales and the innovation." to appear.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] Masuyuki Hitsuda: "Canonical represrntations of Gaussian peocesses and inteqreal operators." to appear in “Proceedings of Random Fields" World Scientific. (1992)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] Yoichi Oshima: "On conservativeness and recurrence criteria for Markov processes." to appear in “Ptential Analvsis".

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] Yoichi Oshima: "On a construction of Markov processes associated with time dependent Dirichret spaces." to appear in“Forum Math".

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] Yukimasa Oka: "A note on ergodic states Cーdvnamics." Kumamoto J.Math.4. 1-4 (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] Yasumasa Saisho,Hideki Tanemura: "Pitman tvpe theorem for oneーdimensional diffusion processes." Tokyo J.Math.13. 429-440 (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] Takeyuki Hida,Masuyuki Hitsuda: "Gaussian processesーRepresentations and Applications." American Math.Soc., (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] Masuyuki Hitsuda: "Canonical representation of Gaussian semimartingales and the innovation."

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] Masuyuki Hitsuda: "Canonical representations of Gaussian processes and integral operators." " Proceedings of Gaussian Random Fields".

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] Yoichi Oshima: "On conservativeness and recurrence criteria for Markov processes." "Potential Analysis".

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] Yichi Oshima: "On a construction of Markov processes associated with time dependent Dirichret spaces." "Forum Math. ".

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] Yukimasa Oka: "A note on ergodic states on C^*-dynamics." Kumamoto J. Math.Vol. 4. 1-4 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] Yasumasa Saisho: "Pitman type theorem for one-dimensional diffusion processes." Tokyo J. Math.Vol. 13. 429-440 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] Takeyuki Hida , Masuyuki Hitsuda: American Math. Soc.Gaussian processes --- Representations and Application.,

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] Masuyuki Hitsuda: "Canonical representation of Gaussian semimartingales and the innovation."

    • Related Report
      1990 Annual Research Report
  • [Publications] Masuyuki Hitsuda: "Canonical representations of Gaussian processes and integral operators." to appear in “Proceedings of Gaussian Random Fielde",World Scientific.(1992)

    • Related Report
      1990 Annual Research Report
  • [Publications] Yoichi Oshima: "On conservativeness and recurrence criteria for Markov processes." “Potential Analysis".

    • Related Report
      1990 Annual Research Report
  • [Publications] Yoichi Oshima: "On a construction of Markov processes associated with time dependent Dirichret spaces." “Forum Math.".

    • Related Report
      1990 Annual Research Report
  • [Publications] Yukimasa Oka: "A note on ergodic states on Cーdynamics." Kumamoto J.Math.4. 1-4 (1991)

    • Related Report
      1990 Annual Research Report
  • [Publications] Yasumasa Saisho: "pitman type theorem for oneーdimensional diffusion processes." Tokyo J.Math.13. 429-440 (1991)

    • Related Report
      1990 Annual Research Report
  • [Publications] Takeyuki Hida Masuyuki Hitsuda: "Gaussian processesーーーRepresentation and Applications." American Math.Soc.,

    • Related Report
      1990 Annual Research Report
  • [Publications] Y.Oshima: "On cors ervativeness and recurrence ciriteria for Markov processes."

    • Related Report
      1989 Annual Research Report
  • [Publications] M.Fukushima: "On the skew product of symmetric Markov processes." Forum Math.1. 103-142 (1989)

    • Related Report
      1989 Annual Research Report
  • [Publications] T.Hida: "Gaussian processes---Representations and Applications" American Mathematical Society, 200 (1990)

    • Related Report
      1989 Annual Research Report

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Published: 1990-04-01   Modified: 2016-04-21  

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