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Representation of stochastic processes and the limit theorem.

Research Project

Project/Area Number 60540141
Research Category

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

Allocation TypeSingle-year Grants
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionFaculty of Science, Kumamoto University

Principal Investigator

HITSUDA Masuyuki  Faculty of Science, Kumamoto University, 理学部, 教授 (50024237)

Co-Investigator(Kenkyū-buntansha) OKA Yukimasa  Faculty of Science, Kumamoto University, 理学部, 助教授 (50089140)
OSHIMA Yoichi  Faculty of Engineering, Kumamoto University, 工学部, 教授 (20040404)
KOHNO Mitsuhiko  Faculty of Science, Kumamoto University, 理学部, 教授 (30027370)
TAKADA Yoshikazu  Faculty of Science, Kumamoto University, 理学部, 講師 (70114098)
YOSHIDA Kiyoshi  Faculty of Science, Kumamoto University, 理学部, 助教授 (80033893)
Project Period (FY) 1985 – 1986
Project Status Completed (Fiscal Year 1986)
Budget Amount *help
¥1,600,000 (Direct Cost: ¥1,600,000)
Fiscal Year 1986: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 1985: ¥800,000 (Direct Cost: ¥800,000)
KeywordsGaussian processes / canonical representation / innovation / Bruwnian motoon / ホワイトノイズ
Research Abstract

Under the title "Representation of Stochastic processes and the limit theorem", we have well organized a research system on mathematical analysis, and we could obtain many results in wide fields. The main contents are (1) Representaion of Gaussian processes, (2) Mouvements of infinite particles and the limit theorem, (3) Analysis of Markov processes by means of Dirichlet forms, and(4) Data analysis in the field of probability theory, and moreover (5) Global analvsis of ordinary differentian equations and the numerical treatment, (6) Super-sub solutions of elliptic partial differential equations of non linear type, in the field of functional equations. The head investigator concerns representation theory of Gaussian processes and the limit behavior of infinitely many interacting particles. Some new sufficient conditions for a Gaussian process to have tha single innovations has been obtained.

Report

(1 results)
  • 1986 Final Research Report Summary
  • Research Products

    (11 results)

All Other

All Publications (11 results)

  • [Publications] M.Hitsuda;I.Mitoma: J.of Mult.Anal.19. 311-328 (1986)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] Y.Oshima: Lecture Notes in Mathematics.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] Y.Oshima: Lecture Notes in Mathematics.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] Y.Takada: Sequential Analysis. 5. 93-101 (1986)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] M.Kohno: Funkcialaj Ekvacioj.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] K.Yoshida;Fukagai;Kusano: J.of Math.Anal.Appl.122. (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] Hitsuda, I. mitoma: "Tightness problem and evolution equation arising from fluctuation phenomena for interacting particles." J. of Mult. Anal.19. 311-328 (1986)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] Osima: "On a transformation of symmetric Markov process and recurrence property." Lecture Notes in Math.to appear.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] Y. Oshima: "On absolutely continuity of two symmetric Markov processes." Lecture Notes in Math.to appear.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] Y. Takada: "Non existence of fixed sample size procedures for scale families." Sequential Analysis. 5. 93-101 (1986)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] M. Kohno: "A connection problem for hypergeometric systems." Funkcialaj Ekvacioj. to appear.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1986 Final Research Report Summary

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Published: 1987-03-31   Modified: 2016-04-21  

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