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2006 Fiscal Year Final Research Report Summary

Theory of stable stochastic processes and generation of random numbers of stable type

Research Project

Project/Area Number 16540130
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 InstitutionOkayama University of Science

Principal Investigator

TAKENAKA Shigeo  Okayama University of Science, Professor, 理学部, 教授 (80022680)

Co-Investigator(Kenkyū-buntansha) TAKASHIMA Keizo  Okayama University of Science, Professor, 理学部, 教授 (00137184)
KOJO Katsuya  Niihama Junior College, Associate Professor, 理数科, 助教授 (10280471)
Project Period (FY) 2004 – 2006
Keywordsstochastic processes of stable type / maultiple markov properties / random numbers / stable random numbers
Research Abstract

1) Kojo has investigated the relations between some 2-dimensional stable distributions and their marginal distributions. Different from Gaussian case, he found that there exist 2-dimensional stable distributions which are completely different as 2-dimensional distributions but they share the same marginal distributions in any directions.
2) Takenaka proposed a new method of generating stable random numbers. At the first, we have to notice that the usual method of random generation by computer programs can not approximate the heavy tail of the stable distributions. Using the "Recursive Call" technique, we can obtain algorithms which approximate the tail much better than usual methods. More over, the overhead time for the recursive call is only 10%.
The results are presented several conferences of colloquims ;
2005 March, Manheim University
2006 March, Berlin Weierstrass institute, Jena University
2006 June Vilnius Conference
2006 Nov. Mejo University, Tokyo Rika University

  • Research Products

    (12 results)

All 2006 2005 2004

All Journal Article (12 results)

  • [Journal Article] 安定型乱数の発生について2006

    • Author(s)
      林聡美, 榎本安宏, 林弘子, 竹中茂夫
    • Journal Title

      統計数理研究所共同研究リポート 184

      Pages: 89-101

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] On generation of stable random numbers (in Japanese)2006

    • Author(s)
      Hayashi, Satomi ; Enomoto, Yasuhiro ; Hayashi, Hiroko, Takenaka, Shigeo
    • Journal Title

      The Institute of Statistical Mathematics Cooperative Research Report 184

      Pages: 89-101

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Two-dimensional Symmetric Stable Distributions and their Projections2005

    • Author(s)
      Katsuya Kojo
    • Journal Title

      Nagoya Math. J. 180

      Pages: 135-149

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] 離散時間パラメータ対称安定過程の多重マルコフ性と標準表現について2005

    • Author(s)
      古城克也
    • Journal Title

      統計数理研究所共同研究リポート 175

      Pages: 102-109

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Two-dimensional Symmetric Stable Distributions and their Projections2005

    • Author(s)
      Kojo, Katsuya
    • Journal Title

      Nagoya Mathematical Journal 180

      Pages: 135-149

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] On the multiple markov properties of discrete parameter symmetric stable processes and their canonical representations2005

    • Author(s)
      Kojo, Katsuya
    • Journal Title

      The Institute of Statistical Mathematics Cooperative Research Report 175

      Pages: 102-109

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Generation of Random Numbers with Heavy Tailed Distribution2004

    • Author(s)
      林聡美, 竹中茂夫
    • Journal Title

      統計数理研究所共同研究リポート 170

      Pages: 63-70

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] 裾の重い分布に従う乱数の発生2004

    • Author(s)
      林聡美, 竹中茂夫
    • Journal Title

      岡山理科大学紀要 40

      Pages: 1-7

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] 特定の1次元射影から決定される2次元対称安定分布について2004

    • Author(s)
      古城克也
    • Journal Title

      統計数理研究所共同研究リポート 170

      Pages: 71-109

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Generation of Random numbers with Heavy tailed Distributions2004

    • Author(s)
      Hayashi, Satomi, Takenaka, Shigeo
    • Journal Title

      The Institute of Statistical Mathematics Cooperative Research Report 170

      Pages: 63-70

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Generation of Random numbers with Heavy tailed Distributions (in Japanese)2004

    • Author(s)
      Hayashi, Satomi, Takenaka, Shigeo
    • Journal Title

      The bulletin of Okayama University of Science 40

      Pages: 1-7

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] On two dimensional stable distriburions which are determined by their 1-dimensional projections (in Japanese)2004

    • Author(s)
      Kojo, Katsuya
    • Journal Title

      The Institute of Statistical Mathematics Cooperative Research Report 170

      Pages: 71-109

    • Description
      「研究成果報告書概要(欧文)」より

URL: 

Published: 2008-05-27  

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