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

2007 Fiscal Year Final Research Report Summary

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
KeywordsU-statistics / V-statistics / Degenerate kernel / Weakly dependent / Strongly dependent / Mathematical finance / Fractional Brownian motion / Reflecting Brownian motion
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.

  • Research Products

    (31 results)

All 2007 2006 2005 2004

All Journal Article (12 results) (of which Peer Reviewed: 6 results) Presentation (18 results) Book (1 results)

  • [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
    • 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
    • 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
  • [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
  • [Journal Article] Numerical simulation of reflecting geometrical Brownian motion and its application to mathematical finance2005

    • Author(s)
      S.Kanagawa
    • Journal Title

      Nonlinear Analysis 63

      Pages: e2209-e2222

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

      Pages: e2209-e2222

    • Description
      「研究成果報告書概要(欧文)」より
  • [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
  • [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
  • [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
    • Year and Date
      20070900
    • Description
      「研究成果報告書概要(和文)」より
  • [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)
    • Year and Date
      20070530-0602
    • Description
      「研究成果報告書概要(和文)」より
  • [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
    • Year and Date
      20070530-0602
    • Description
      「研究成果報告書概要(欧文)」より
  • [Presentation] Fuzzy Information Analysis Applying AIC Method2006

    • Author(s)
      S. Kanagawa
    • Organizer
      SCIS & ISIS2006
    • Place of Presentation
      Tokyo Institute of Technology
    • Year and Date
      20060920-24
    • Description
      「研究成果報告書概要(欧文)」より
  • [Presentation] Decision method of optimal fuzzy graph applying fuzzy decision2006

    • Author(s)
      S.Kanagawa
    • Organizer
      ICM 2006
    • Place of Presentation
      Madrid
    • Year and Date
      20060822-30
    • Description
      「研究成果報告書概要(和文)」より
  • [Presentation] Approximation theorems for random permanents defined by functionals2006

    • Author(s)
      S. Kanagawa
    • Organizer
      WORKSHOP ON PROBABILITY WITH APPLICATIONS
    • Place of Presentation
      Taipei
    • Year and Date
      20060605-09
    • Description
      「研究成果報告書概要(欧文)」より
  • [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
    • Year and Date
      20060300
    • Description
      「研究成果報告書概要(和文)」より
  • [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
  • [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
    • Year and Date
      20051220-22
    • Description
      「研究成果報告書概要(和文)」より
  • [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
    • Year and Date
      20051031-1104
    • Description
      「研究成果報告書概要(和文)」より
  • [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
    • Year and Date
      20050801-05
    • Description
      「研究成果報告書概要(和文)」より
  • [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
    • Year and Date
      20050801-05
    • Description
      「研究成果報告書概要(欧文)」より
  • [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)
    • Year and Date
      20040630-0707
    • Description
      「研究成果報告書概要(和文)」より
  • [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)
    • Year and Date
      20040616-19
    • Description
      「研究成果報告書概要(和文)」より
  • [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
    • Year and Date
      20040616-19
    • Description
      「研究成果報告書概要(欧文)」より
  • [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
    • Year and Date
      20040200
    • Description
      「研究成果報告書概要(和文)」より
  • [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
    • Year and Date
      20040100
    • Description
      「研究成果報告書概要(和文)」より
  • [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
    • Year and Date
      20040100
    • Description
      「研究成果報告書概要(和文)」より
  • [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

URL: 

Published: 2010-02-04  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi