• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

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
Project Status Completed (Fiscal Year 2006)
Budget Amount *help
¥2,700,000 (Direct Cost: ¥2,700,000)
Fiscal Year 2006: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2005: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2004: ¥1,000,000 (Direct Cost: ¥1,000,000)
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

Report

(4 results)
  • 2006 Annual Research Report   Final Research Report Summary
  • 2005 Annual Research Report
  • 2004 Annual Research Report
  • Research Products

    (25 results)

All 2006 2005 2004

All Journal Article (25 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
    • Related Report
      2006 Final Research Report Summary
  • [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
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] 安定型乱流の発生について。2006

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

      統計数理研究所リポート 184

      Pages: 89-101

    • Related Report
      2006 Annual Research Report
  • [Journal Article] 新しいハッシュ関数SSI160の構築2006

    • Author(s)
      谷口礼偉, 上田澄江, 高嶋恵三
    • Journal Title

      Research Memorandum 986

      Pages: 12-12

    • Related Report
      2006 Annual Research Report
  • [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

      無限分解可能過程に関連する諸問題(10) 統計数理研究所共同研究リポート (3月発行掲載確定)

      Pages: 13-13

    • Related Report
      2005 Annual Research Report
  • [Journal Article] 安定型乱数の発生について2006

    • Author(s)
      林弘子
    • Journal Title

      岡山理科大学2005年度修士論文

      Pages: 24-24

    • Related Report
      2005 Annual Research Report
  • [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
    • Related Report
      2006 Final Research Report Summary
  • [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
    • Related Report
      2006 Final Research Report Summary
  • [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
    • Related Report
      2006 Final Research Report Summary
  • [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
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] 裾の重い分布に従う乱数の発生2005

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

      岡山理科大学紀要(2004年付け、発行2005年3月) 40-A

      Pages: 1-7

    • NAID

      110001244621

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Two-dimensional symmetric stable distributions and their projections.2005

    • Author(s)
      K.Kojo
    • Journal Title

      Nagoya Mathematical Journal 180

      Pages: 135-149

    • Related Report
      2005 Annual Research Report
  • [Journal Article] 離散時間パラメーター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

      無限分解可能過程に関連する諸問題(9) 統計数理研究所共同研究リポート 175

      Pages: 110-115

    • Related Report
      2005 Annual Research Report
  • [Journal Article] 安定分布の吸引域に入る乱数の生成2005

    • Author(s)
      榎本安宏
    • Journal Title

      岡山理科大学2004年度修士論文

      Pages: 28-28

    • Related Report
      2004 Annual Research Report
  • [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
    • Related Report
      2006 Final Research Report Summary
  • [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

    • NAID

      110001244621

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [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
    • Related Report
      2006 Final Research Report Summary
  • [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
    • Related Report
      2006 Final Research Report Summary
  • [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
    • Related Report
      2006 Final Research Report Summary
  • [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
    • Related Report
      2006 Final Research Report Summary
  • [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 40A(掲載予定)

      Pages: 8-8

    • NAID

      110001244621

    • Related Report
      2004 Annual Research Report
  • [Journal Article] 離散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2004

    • Author(s)
      古城克也
    • Journal Title

      統計数理研究所共同研所リポート 無限分解可能過程に関する諸問題(8) (掲載予定)

      Pages: 8-8

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Diffusion-Approximations for Navier-Stokes Equation in Space-Time Gaussian Velocity Field2004

    • Author(s)
      H.Watanabe
    • Journal Title

      Stochastic Analysis and Applications 22

      Pages: 1363-1384

    • Related Report
      2004 Annual Research Report
  • [Journal Article] The Character table of the hecke algebra H(GL2(Fq),A), where A is the split torus2004

    • Author(s)
      H.Hashizume, Y.Mori
    • Journal Title

      Osaka journal of Mathematics 41

      Pages: 793-818

    • Related Report
      2004 Annual Research Report
  • [Journal Article] The structure of the Hecke algebras of GL2(Fq) relative to the split torus and its normalizer2004

    • Author(s)
      Y.Mori
    • Journal Title

      Hiroshima Mathematical Journal 34

      Pages: 127-145

    • Related Report
      2004 Annual Research Report

URL: 

Published: 2004-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi