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Limit theorems for U- and V-statistics for dependent random variables and their applications

Research Project

Project/Area Number 16540124
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 InstitutionMusashi Institute of Technology

Principal Investigator

KANAGAWA Shuya  Musashi Institute of Technology, Faculty of Engineering, Professor (50185899)

Co-Investigator(Kenkyū-buntansha) MAESONO Yoshihiko  Kyushu University, Faculty of Science, Department of Mathematics, Professor (30173701)
SAISHO Yasumasa  Hiroshima University, Faculty of Engineering, Department of Applied Mathematics, Associate Professor (70195973)
INOUE Koichi  Musashi Institute of Technology, Faculty of Engineering, Associate Professor (50232533)
FURUTA Koji  Musashi Institute of Technology, Faculty of Engineering, Associate Professor (80257104)
Project Period (FY) 2004 – 2007
Project Status Completed (Fiscal Year 2007)
Budget Amount *help
¥3,840,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥240,000)
Fiscal Year 2007: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2006: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2005: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2004: ¥1,200,000 (Direct Cost: ¥1,200,000)
KeywordsU-statistics / V-statistics / Degenerate kernel / Weakly dependent / Strongly dependent / Mathematical finance / Fractional Brownian motion / Reflecting Brownian motion / 確率論 / 統計数学 / シミュレーション工学 / 情報基礎 / 解析学1 / ノンパラメトリック統計学 / 非線形解析学 / 金融工学 / 多重ウィナー積分
Research Abstract

The author investigated limit theorems for symmetric statistics(U-statistics and V-statistics) for dependent random variables using new technique by applying limit theorems for Banach space valued i.i.d. random variables. Usually well known Hoeffding's decomposition for symmetric scholastics cannot be used for symmetric statistics with non-degenerate kernels. Furthermore we tried some simulations of such dependent random variables satisfying some mixing conditions or strongly dependence. The simulation can be applied to mathematical finance under some dependent conditions.
The author focused on the distribution of pseudo-random numbers which are used for numerical application of such approximate solutions and consider the error estimation of the Euler-Maruyama approximation when the distribution of underlying random variables is different from the normal distribution. Furthermore some results for stochastic differential equations with boudary conditions on multi-dimensional domains(so-called Skorohod SDE) are obtained. We define an approximate solution of stochastic differential equation(SDE) with a reflecting barrier using the penalty method and estimate error of the approximate solution. In this note we have two aims. One is to define the approximate solution using not only a sequence of increments of Brownian motion which is independent and has normal distribution but also dependent sequence that does not obey normal distribution. Another one is, to show the advantage of the penalty method, we observe sample paths of Brownian motion with a soft boundary, i.e. any path of the Brownian motion does not reflect at the bundary immediately but is absorbed for a short period according to the strength of the path getting out of the boundary.

Report

(5 results)
  • 2007 Annual Research Report   Final Research Report Summary
  • 2006 Annual Research Report
  • 2005 Annual Research Report
  • 2004 Annual Research Report
  • Research Products

    (49 results)

All 2008 2007 2006 2005 2004

All Journal Article (27 results) (of which Peer Reviewed: 8 results) Presentation (20 results) Book (2 results)

  • [Journal Article] An Edgewoth expansion and a normalizing transformation for L-statistics2008

    • Author(s)
      Y.Maesono
    • Journal Title

      Bulletin of Informatics and Cyberneticsに 掲載予定

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A stochastic model describing the number of male insects which are left without partners2007

    • Author(s)
      Y.Saisho
    • Journal Title

      Ecological Modelling 207

      Pages: 5-14

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Fuzzy Clustering Level Analysis applying AIC Method2007

    • Author(s)
      S.Kanagawa, H.Uesu, K.Shinkai, E.Tsuda
    • Journal Title

      Journal of Sdvanced Computational Intelligence and intelligent Informatics (出版決定)

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Fuzzy Clustering Level Analysis Using AIC Method for Large Size Samples2007

    • Author(s)
      S.Kanagawa, H.Uesu, K.shinkai, E.Tsuda
    • Journal Title

      Proceedings ICICIC2007, Kymamaaoto (出版決定)

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Nonlinear Schrodinger equations for envelope functions induced from nearly bichromatic waves with random spectrum2006

    • Author(s)
      S.Kanagawa
    • Journal Title

      Proc.Neural, Parallel and Scientific Computations 15

      Pages: 89-92

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Approximate solution of reflecting Brownian motion using penalty method and numerical application to imperfect elastic barrier2006

    • Author(s)
      S.Kanagawa
    • Journal Title

      Dynamic Systems and Applications 15

      Pages: 287-300

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Nonlinear Schrodinger equations for envelope functions induced from nearly bichromat induced from nearly bichromatic waves with random spectrums2006

    • Author(s)
      S. Kanagawa
    • Journal Title

      Proc. Neural, Parallel and Scientific Computations Vol.3

      Pages: 89-92

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Approximate solution of reflecting Brownian motion using penalty method and numerical application to imperfect elastic barrier2006

    • Author(s)
      S. Kanagawa
    • Journal Title

      Dynamic Systems and Applications Vol.15

      Pages: 287-300

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Approximate solution of reflecting Brownian motion using penalty method and numerical application to imperfect elastic barrier2006

    • Author(s)
      S.Kanagawa, Y.Saisho, H.Uesu
    • Journal Title

      Dynamic Systems and Applications 15

      Pages: 287-300

    • Related Report
      2006 Annual Research Report
  • [Journal Article] On nonlinear Schrodinger equations induced from nearly bichromatic waves with random spectrums2006

    • Author(s)
      S.Kanagawa, T.Nohara, A.Ariomoto, K.Tchizawa
    • Journal Title

      Proceedings of Third International Congerence on Neural,Parallel & Scientific Computations 3

      Pages: 89-92

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Numerical simulation of reflecting geometrical Brownian motion and its application to mathematical finance2005

    • Author(s)
      S.Kanagawa
    • Journal Title

      Nonlinear Analysis 63

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] フィッシャーの情報量,研究ノート2005

    • Author(s)
      竹中 淑子
    • Journal Title

      三田学会雑誌 18

      Pages: 95-104

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Mean square approximation of multi dimensional reflecting fractional Brownian motion via penalty method2005

    • Author(s)
      S.Kanagawa
    • Journal Title

      Discrete and Continuous Dynamical Systems (Supplement Volume)

      Pages: 463-475

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Numerical solution of the stochastic differential equation,2-applications2005

    • Author(s)
      S.Kanagawa
    • Journal Title

      Sugaku Expositions, Amer.Math.Soc 18

      Pages: 75-99

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] 従属確率変数列に対する対称統計量の極限定理について2005

    • Author(s)
      金川 秀也
    • Journal Title

      統計数理研究所共同研究レポート 10

      Pages: 24-42

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Numerical simulation of reflecting geometrical Brownian motion and its application to mathematical finance2005

    • Author(s)
      S. Kanagawa
    • Journal Title

      Nonlinear Analysis Vol.63

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Mean square approximation of multi dimensional reflecting fractional Brownian motion via penalty method2005

    • Author(s)
      S. Kanagawa
    • Journal Title

      Discrete and Continuous Dynamical Systems, Supplement Volume

      Pages: 463-475

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Numerical solution of the stochastic differential Equation2005

    • Author(s)
      S. Kanagawa, S. Ogawa
    • Journal Title

      Sugaku Expositions, Amer. Math. Soc. Vol.18

      Pages: 75-99

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] フィッシャーの情報量,研究ノート2005

    • Author(s)
      竹中淑子, 金川秀也
    • Journal Title

      三田学会雑誌 95

      Pages: 75-99

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Numerical solution of the stochastic differential equation, 2-applications2005

    • Author(s)
      S.Kanagawa, S.Ogawa
    • Journal Title

      Sugaku Expositions, Amer.Math.Soc. 18

      Pages: 75-99

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Mean square approximation of multi dimensional reflecting fractional Brownian motion via penalty method2005

    • Author(s)
      S.Kanagawa, K.Inoue, A.Arimoto, Y.Saisho
    • Journal Title

      Discrete and Continuous Dynamical Systems Supplement Volume

      Pages: 75-99

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Numerical simulation of reflecting geometrical Brownian motion and its application to mathematical finance2005

    • Author(s)
      S.Kanagawa, A.Arimoto, Y.Saisho
    • Journal Title

      Nonlinear Analysis 63

      Pages: 2209-2222

    • Related Report
      2005 Annual Research Report
  • [Journal Article] 従属確率変数列に対する対称統計量の極限定理2005

    • Author(s)
      金川秀也
    • Journal Title

      統計数理研究所共同研究レポート 175

      Pages: 24-42

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Strong Approximation of Reflecting Brownian Motion Using Penalty Method and its Approximation2005

    • Author(s)
      K.Inoue, S.Kanagawa
    • Journal Title

      Proceedings of Neural, Parallel & Scientific Computations (発表予定)

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Numerical solution of the stochastic differential equation, 2-applications2005

    • Author(s)
      S.Kanagawa, S.Ogawa
    • Journal Title

      Sugaku Expositions 19(発表予定)

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Error Estimation for the Euler-Maruyama Approximate Solution of Reflecting Brownian Motion Using Penalty Method and Numerical Applications2005

    • Author(s)
      S.Kanagawa, Y.Saisho, H.Uesu
    • Journal Title

      Journal of Dynamic Systems and Applications (発表予定)

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Numerical Simulation of Reflecting Geometrical Brownian Motion and its Application to Mathematical finance2005

    • Author(s)
      A.Arimoto, S.Kanagawa, Y.Saisho
    • Journal Title

      Nonlinear Analysis (発表予定)

    • Related Report
      2004 Annual Research Report
  • [Presentation] ファジィグラフのシャプレイ値分析と応用II2007

    • Author(s)
      金川 秀也
    • Organizer
      日本数学会2007度秋季総合分科会
    • Place of Presentation
      東北大学
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Numerical analysis for occupation time of some neighborhood of boundary of reflecting Brownian motion2007

    • Author(s)
      S.Kanagawa
    • Organizer
      5th International Conference on Dynamic systems and Applications
    • Place of Presentation
      Atlanta,Georgia,USA.(招待講演)
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Numerical analysis for occupation time of some neighborhood of boundary of reflecting Brownian motion2007

    • Author(s)
      S. Kanagawa
    • Organizer
      5th International Conference on Dynamic systems and Applications
    • Place of Presentation
      Atlanta
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Parameter estimated standardized U-statistics for some dependent sequences2007

    • Author(s)
      S.Kanagawa
    • Organizer
      中華民国数学会
    • Place of Presentation
      台北学術院,台湾
    • Related Report
      2007 Annual Research Report
  • [Presentation] Numerical analysis for occupation time of some neiξhborhood of boundary of reflecting Brownian motion2007

    • Author(s)
      S.Kanagawa
    • Organizer
      5th International Conference on Dynamic systems and Applications
    • Place of Presentation
      Atlanta,USA
    • Related Report
      2007 Annual Research Report
  • [Presentation] Nonlinear Schrodinger equations for envelope functions induced from nearly bichromatic waves with random spectrums2006

    • Author(s)
      S. Kanagawa
    • Organizer
      The Third International Conference on Neural, Parallel & Scientific Computations
    • Place of Presentation
      ATLANTA, U.S.A., AUGUST
    • Year and Date
      2006-09-12
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Decision method of optimal fuzzy graph applying fuzzy decision2006

    • Author(s)
      S.Kanagawa
    • Organizer
      ICM 2006
    • Place of Presentation
      Madrid
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] 0n nonlinear Schrodinger equation induced from nearly bichromatic waves2006

    • Author(s)
      金川 秀也
    • Organizer
      日本数学会2006年度年会
    • Place of Presentation
      中央大学
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Approximation theorems for random permanents defined by functionals2006

    • Author(s)
      S. Kanagawa
    • Organizer
      WORKSHOP ON PROBABILITY WITH APPLICATIONS
    • Place of Presentation
      Taipei
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Fuzzy Information Analysis Applying AIC Method2006

    • Author(s)
      S. Kanagawa
    • Organizer
      SCIS & ISIS2006
    • Place of Presentation
      Tokyo Institute of Technology
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Parameter estimated standardized U-statistics for some dependent sequences2005

    • Author(s)
      金川 秀也
    • Organizer
      科研費シンポジウム「統計数理の基礎理論について」
    • Place of Presentation
      鹿児島大学
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Nonlinear Schrodinger equation for nearly bichromatic waves induced by wave equations2005

    • Author(s)
      S.Kanagawa
    • Organizer
      京都大学数理解析研究所研究集会「関数方程式の解のダイナミクスと数値シミュレーション」
    • Place of Presentation
      京都大学数理解析研究所
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] On nonlinear Schrodinger equations induced from nearly bichromatic waves2005

    • Author(s)
      S.Kanagawa
    • Organizer
      The First Conference on Differential & Difference Equations, Florida Institute of Technology
    • Place of Presentation
      Melbourne,Florida
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] On nonlinear Schrodinger equationas induced from nearly bichromatic waves2005

    • Author(s)
      S. Kanagawa
    • Organizer
      The First Conference on Differential & Difference Equations
    • Place of Presentation
      Florida
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Simulation of reflecting Brownian motion path with soft boundaries using penalty method2004

    • Author(s)
      S.Kanagawa
    • Organizer
      Fourth World Congress of Nonlinear Analysis, 2004
    • Place of Presentation
      Orlando,Florida(招待講演)
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Simulation of reflecting Brownian motion path with soft boundaries using penalty method2004

    • Author(s)
      S.Kanagawa
    • Organizer
      AIMS'Fifth International Conference on Dynamical Systems and Differential Equations California State Polytehnic University
    • Place of Presentation
      Pomona,California(招待講演)
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] ファジィクラスタリングのレベル分析2004

    • Author(s)
      津田 栄
    • Organizer
      日本知能情報ファジィ学会ソフトサイエンス研究会
    • Place of Presentation
      早稲田大学
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Harmonious Fosterage of Human Resources for Training Researchers and the Curriculum Vision2004

    • Author(s)
      I.Kitagaki
    • Organizer
      2004 Hawaii International Conference on Education
    • Place of Presentation
      Hawaii,USA
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Some limit theorems of U-,V-statistics for strongly dependent random variables2004

    • Author(s)
      金川 秀也
    • Organizer
      科研費シンポジウム「確率論における極限定理」
    • Place of Presentation
      九州大学
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Euler-Maruyama approximate solution of reflecting fractional Brownian motion using penalty method2004

    • Author(s)
      S. Kanagawa
    • Organizer
      AIMS' Fifth International Conference on Dynamical Systems and Differential Equations
    • Place of Presentation
      California
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Book] やさしい統計-いかにして統計データを有効利用するか2007

    • Author(s)
      吉原 健一
    • Total Pages
      184
    • Publisher
      培風館
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Book] やさしい統計-いかにして統計データを有効利用するか2007

    • Author(s)
      金川 秀也
    • Total Pages
      177
    • Publisher
      培風館
    • Related Report
      2007 Annual Research Report

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

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