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Study of precise Monte Carlo integration

Research Project

Project/Area Number 26400133
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Basic analysis
Research InstitutionOsaka University

Principal Investigator

Sugita Hiroshi  大阪大学, 理学研究科, 教授 (50192125)

Co-Investigator(Renkei-kenkyūsha) Takanobu Satoshi  金沢大学, 大学院自然科学研究科, 教授 (40197124)
Project Period (FY) 2014-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Keywordsモンテカルロ積分 / ランダム・ワイル・サンプリング / 対独立同分布確率変数列 / k-対独立同分布確率変数列 / k対独立
Outline of Final Research Achievements

Utilizing the fact that the law of large numbers holds for pairwise i.i.d. random variables, we realized a rigorous Monte Carlo integration, called Random Weyl sampling (RWS), with extremely reduced randomness. In this reserch, we developed a k-wise i.i.d. sampling method, which is an extension of RWS and is useful for practice. The method can compute the k-th moment of the sample mean precisely.

Report

(5 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Research-status Report
  • 2015 Research-status Report
  • 2014 Research-status Report
  • Research Products

    (11 results)

All 2018 2017 2016 2014 Other

All Journal Article (1 results) (of which Peer Reviewed: 1 results,  Open Access: 1 results) Presentation (2 results) Book (3 results) Remarks (5 results)

  • [Journal Article] Random Weyl sampling—A secure Monte Carlo integration method2016

    • Author(s)
      Hiroshi SUGITA
    • Journal Title

      Nonlinear Theory and Its Applications, IEICE

      Volume: 7 Issue: 1 Pages: 2-13

    • DOI

      10.1587/nolta.7.2

    • NAID

      130005117781

    • ISSN
      2185-4106
    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Open Access
  • [Presentation] 確率論と計算機科学---乱数と擬似乱数を中心として2018

    • Author(s)
      杉田洋
    • Organizer
      大阪大学確率論セミナー
    • Related Report
      2017 Annual Research Report
  • [Presentation] 確率論と乱数2014

    • Author(s)
      杉田洋
    • Organizer
      大阪大学確率論セミナー
    • Place of Presentation
      大阪大学理学部
    • Year and Date
      2014-10-21
    • Related Report
      2014 Research-status Report
  • [Book] Probability and Random Number: A first guide to randomness2017

    • Author(s)
      Hiroshi SUGITA
    • Total Pages
      140
    • Publisher
      World Scientific
    • ISBN
      9789813228252
    • Related Report
      2017 Annual Research Report
  • [Book] Probability and Random Number2017

    • Author(s)
      Hiroshi Sugita
    • Total Pages
      140
    • Publisher
      World Scientific
    • Related Report
      2016 Research-status Report
  • [Book] 確率と乱数2014

    • Author(s)
      杉田洋
    • Total Pages
      140
    • Publisher
      数学書房
    • Related Report
      2014 Research-status Report
  • [Remarks] モンテカルロ法,乱数,および疑似乱数

    • URL

      http://www.math.sci.osaka-u.ac.jp/~sugita/mcm.html

    • Related Report
      2017 Annual Research Report 2016 Research-status Report
  • [Remarks] Monte Carlo method, random number, and ...

    • URL

      http://www.math.sci.osaka-u.ac.jp/~sugita/mcm_E.html

    • Related Report
      2017 Annual Research Report
  • [Remarks] Monte Carlo Method, Random Number, and ...

    • URL

      http://www.math.sci.osaka-u.ac.jp/~sugita/mcm_E.html

    • Related Report
      2016 Research-status Report
  • [Remarks] Hiroshi SUGITA Works in Mathematics

    • URL

      http://www.math.sci.osaka-u.ac.jp/~sugita/mathematics.html

    • Related Report
      2015 Research-status Report
  • [Remarks] Hiroshi SUGITA Work in Mathematics

    • URL

      http://www.math.sci.osaka-u.ac.jp/~sugita/mathematics.html

    • Related Report
      2014 Research-status Report

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Published: 2014-04-04   Modified: 2019-03-29  

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