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Variations of random fields and application to computation

Research Project

Project/Area Number 12640136
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionAichi Prefectural University

Principal Investigator

SI Si  Aichi Prefectural University, Faculty of Information Science technology, Department of applied information Science and Technology, Associate Professor, 情報科学部, 助教授 (70269687)

Co-Investigator(Kenkyū-buntansha) HIDA Takeyuki  Meijo University, Faculty of Science and Technology, Professor, 理工学部, 教授(特任) (90022508)
Project Period (FY) 2000 – 2001
Project Status Completed (Fiscal Year 2001)
Budget Amount *help
¥2,100,000 (Direct Cost: ¥2,100,000)
Fiscal Year 2001: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2000: ¥1,200,000 (Direct Cost: ¥1,200,000)
Keywordswhite noise / innovation / random field / Gaussian / Markov property / subordination / white noise
Research Abstract

The plan during the research period (2000 - 2001 academic year) is to study random fields and related problems of computation. The main results have been obtained are all based on the Innovation Theory, which provides useful tools of study. The results are as follows.
1. Gaussian random fields.
The innovation of a Gaussian random field parameterized by a contour or a closed surface can be obtained by its variation. Usually, such an innovation is a white noise, by which the given field is expressed as a stochastic integral. The kernel represents the probabilistic properties of the field like way of dependence including reversibility when the parameters are ordered.
2. General random fields.
For a field expressed as an integral of homogeneous chaos we can form innovations explicity, so that the best predictor is obtained. Also, random linear functions of a general additive process allow us to form innovation in a nonlinear manner, and we solved the computability problems, like jump finding, m the theory of communications.
3. Application of white noise theory.
Having had profound study on the subordination for additive processes, we applied to the processing of the X-ray data from the black-hole candidate. Beyond the spectrum we have computed its characteristic functional to have a good mathematical model.

Report

(3 results)
  • 2001 Annual Research Report   Final Research Report Summary
  • 2000 Annual Research Report

Research Products

(48 results)

All Other

All Publications

  • [Publications] Si Si: "Innovation of the Levy Brownian motion"Volterra Center Notes, Roma University. N.475. 1-9 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Si Si, Win Win Htay: "Random irreversible phenomenon ; Entropy in subordination"Chaos, Solitons & Fractals, Elsevier Science. Vol.12. 2873-2876 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Si Si: "Entropy in subordination and Filtering"Acta Applicandae Mathemathecae, Kluwer Academic Publishers. Vol.63. 433-439 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T.Hida: "Innovation approach to Stochastic processes and Quantum Dynainics"Quantum Probability and White noise analysis. Vol XIII. 161-169 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T.Hida: "Complexity and irreversibility in stochastic analysis"Chaos, Solitons & Fractals, Elsevier Science. Vol 12. 2859-2863 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] L.Accardi, T.Hida, H.-H.Kuo: "The Ito tabale of the square of white noise"Infinite Dimensional Analysis, Quantum Prob. And Related Topics. Vol.4, No.2. 267-275 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] L.Accardi, H-H.Kuo, N.Obata, K.Saito, Si Si, L.Streit(編集): "Selected Papers of Takeyuki Hida"World Scientific Publishing Co.. 480 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] L.Accardi, H-H.Kuo, N.Obata, K.Saito, Si Si, L.Streit(編集): "Recent Developments in infinite-Dimensional Analysis and Quantum Probability"Kluwer Academic Publishers. 464 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] L. Accardi, H-H. Kuo, N. Obata, K. Saito, Si Si, L. Streit (ed): "Trends in Contemporary Infinite Dimensional Analysis and Quantum Probability"Nakanishi Co. Ltd. Kyoto Italian School of Asian Studies. (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] L. Accardi. H-H. Kuo. N. Obata. K. Saito. Si Si. L. Streit (ed): "Selected Papers of Takeyuki Hida"World Scientific. (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] L. Accardi, H-H. Kuo, N. Obata, K. Saita, Si Si, L. Streit (ed): "Rcent Developments in Infinite Dimensional Analysis and Quantum Probability"Kluwer Academic Publication. (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T. Hida et. al.: "Stocastics in Finite and Infinite Demensions"Birkhauser. (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T. Hida et. al.: "Mathematical hysics and Stochastic Analysis"World Scientific. (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T. Hida and K. Saito (ed): "Quantum Information II"World Scientific. (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T. Hida: "Complexity in white noise"Quantum Information II, World Scientific. 61-70 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T. Hida: "Some methods of computation in white noise"Unconventional Models of Computation, UMC'2K. 85-93 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T. Hida and Si Si: "Elemental random variables in White Noise Theoy : beyond Reductionism, Quantum Information III"World Scientific. 59-66 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T. Hida: "Complexity and irreversibility in stochastic analysis, Chaos, Solitons & Fractals"Elsevier Science. Bol.12. 2859-2863 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T. Hida: "White noise analysis"A new frontier, Volterra Center Notes, Roma University. N.499. 1-15 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T. Hida: "Innovation approach to Stochastic processes and Quantum Dynamics"Quantum Probability and White noise analysis. Vol. XIII. 161-169 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T. Hida and K. Saito (ed): "Quantum Information III"World Scientific. (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] L. Accardi, T. Hida, and H-H. Kuo: "The Ito tabale of the ssquare of white noise"Infinite Dimensional Analysis, Quantum Prob. and Related Topics. Vol.4, No.2. 267-275 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T. Hida: "Laplacians in White noise analysis"Proc. Session in White noise Analysis, Amer. Math. Math. Soc.. (in press). (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T. Hida and Y. Hara: "Mamichi"Quantum Information IV, World Scientific. (in press).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T. Hida and K. Saito (ed): "Quantum Information IV"World Scientific. (in press). (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Si Si: "Gasussian processes and Gaussian random fields"Quantum Information II, World Scientific. 195-204 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Si Si: "Random fields and mutiple Markov properties"Supplementary Papers For the 2^<nd> International conference on Unconventional Models of Computation, UMC'2K, et. I. Antoniou et. al. CDMTCS-147, Center for Discrete Mathematics and Theoretical Computer Science, Solvay Institute. 64-70 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Si Si: "Random ireversibile phenomena, Entropy in subordination, Chaos, solitons & Fractals Vol.12"Elsevier Science. 2873-2876 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Si Si: "Innovation of the Levy Brownian motion"Volterra Center Notes, Roma University. N.475. 1-9 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Si Si and Win Win Htay: "Entropy in subordination and Filtering, Applicandae Mathematheca Vol.63"Kluwer Academic Publishers. 433-439 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Si Si: "Representations and transformations of Gaussian random fields"Quantum Information III, World Scientific. 177-184 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Si Si and Win Win Htay: "Topics on Gaussian random fields"Quantum Information IV, World Scientific. (in press).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Si Si: "Innovation of the Levy Brownian motion"Volterra Center Notes, Roma University. N.475. 1-9 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Si Si, Win Win Htay: "Random irreversible phenomenon ; Entropy in subordination"Chaos, Solitons & Fractals, Elsevier Science. Vol.12. 2873-2876 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Si Si: "Entropy in subordination and Filtering"Acta Applicandae Mathemathecae, Kluwer Academic Publishers. Vol.63. 433-439 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] T.Hida: "Inovation approach to Stochastic processes and Quantum Dynamics"Quantum Probability and White noise analysis. Vol XIII. 161-169 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] T.Hida: "Complexity and irreversibility in stochastic analysis"Chaos, Solitons & Fractals, Elsevier Science. Vol 12. 2859-2863 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] L.Accardi, T.Hida, H.-H.Kuo: "The Ito tabale of the square of white noise"Infinite Dimensional Analysis, Quantum Prob.And Related Topics. Vol.4, No.2. 267-275 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] L.Accardi, H-H Kuo, N.Obata, K.Saito, Si Si, L.Streit(編集): "Selected Papers of Takeyuki Hida"World Scientific Publishing Co.. 480 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] L.Accardi, H-H.Kuo, N.Obata, K.Saito, Si Si, L.Streit(編集): "Recent Developments in infinite-Dimensional Analysis and Quantum Probability"Kluwer Academic Publishers. 464 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Si Si: "Gaussian processes and Gaussian Random fields"Quantum Information. II. 195-204 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Si Si: "Random fields and multiple Markov properties"Supplementary Papers for the 2nd International Conference on Unconventional Models of Computation UMC'2k, Solvay Institute. CDMTCS147. 64-70 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Si Si: "Representations and transformations of Gaussian random fields"Quantum Information. III(近刊). (2001)

    • Related Report
      2000 Annual Research Report
  • [Publications] T.Hida: "Complexity in White Noise Analysis"Quantum Information. II. 61-70 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] T.Hida: "Some methods of computation in White Noise Calculus"Unconventional Models of Computation, UMC'2k, Proceeding of the 2nd Interntional Conference on Unconventional Models of Computation UMC'2k. 85-93 (2001)

    • Related Report
      2000 Annual Research Report
  • [Publications] T.Hida and Si Si: "Elemental random variables in White Noise Theory, beyond Reductionism"Quantum Information. III(近刊). (2001)

    • Related Report
      2000 Annual Research Report
  • [Publications] L.Accardi,H.H.Kuo,N.Obata K.Saito,Si Si,L.Streit: "Trends in Contemporary Infinite Dimensional Analysis and Quantum Probability"Nakanishi Co.Lid.Kyoto, Italian School of Asian Studies. (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] T.Hida: "Quantum Information II"World Scientific. (2000)

    • Related Report
      2000 Annual Research Report

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Published: 2000-03-31   Modified: 2016-04-21  

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