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

Information theoretic study of empirical probability

Research Project

Project/Area Number 22654015
Research Category

Grant-in-Aid for Challenging Exploratory Research

Allocation TypeSingle-year Grants
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionOsaka University

Principal Investigator

FUJIWARA Akio  大阪大学, 理学研究科, 教授 (30251359)

Project Period (FY) 2010 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥3,210,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥1,000,000 (Direct Cost: ¥1,000,000)
Keywords統計数学 / 経験確率 / 情報理論 / ユニバーサル符号化 / ランダムネス / ダイバージェンス
Research Abstract

We explored an information theoretic study of empirical probability. The main results are summarized as follows: 1) A novel Martin-Loef randomness criterion for two distinct computable probability measures was obtained based on finite-type quasi-symmetric divergence functions. 2) An alternative proof of a game-theoretic law of large numbers was given based on the Lynch-Davisson universal coding algorithm, and a possibility of generalizing the law of large numbers and the theorem of convergence of opinions to a general prediction game was pointed out.

Report

(4 results)
  • 2012 Annual Research Report   Final Research Report ( PDF )
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (7 results)

All 2013 2011 2010 Other

All Presentation (6 results) Remarks (1 results)

  • [Presentation] Convex games, randomness, and geometry2013

    • Author(s)
      藤原彰夫
    • Organizer
      研究集会「エルゴード理論,情報理論,計算機科学とその周辺」
    • Place of Presentation
      大阪大学
    • Year and Date
      2013-03-14
    • Related Report
      2012 Final Research Report
  • [Presentation] Convex games, randomness, and geometry2013

    • Author(s)
      藤原彰夫
    • Organizer
      研究集会「エルゴード理論,情報理論,計算機科学とその周辺」
    • Place of Presentation
      大阪大学
    • Related Report
      2012 Annual Research Report
  • [Presentation] Randomness criteria in terms of f-divergences2011

    • Author(s)
      藤原彰夫
    • Organizer
      研究集会「エルゴード理論,情報理論,計算機科学とその周辺」
    • Place of Presentation
      統計数理研究所
    • Year and Date
      2011-03-05
    • Related Report
      2012 Final Research Report
  • [Presentation] Randomness criteria in terms of f-divergences2011

    • Author(s)
      藤原彰夫
    • Organizer
      研究集会「エルゴード理論,情報理論,計算機科学とその周辺」
    • Place of Presentation
      統計数理研究所(東京都)(招待講演)
    • Year and Date
      2011-03-05
    • Related Report
      2010 Annual Research Report
  • [Presentation] Randomness criteria in terms of f-divergences2010

    • Author(s)
      Akio Fujiwara
    • Organizer
      Third workshop on game theoretic probability and related topics
    • Place of Presentation
      Royal Holloway, University of London
    • Year and Date
      2010-06-23
    • Related Report
      2012 Final Research Report
  • [Presentation] Randomness criteria in terms of f-divergences2010

    • Author(s)
      藤原彰夫
    • Organizer
      Third Workshop on Game-Theoretic Probability and Related Topics
    • Place of Presentation
      Royal Holloway, University of London (UK)(招待講演)
    • Year and Date
      2010-06-23
    • Related Report
      2010 Annual Research Report
  • [Remarks]

    • URL

      http://www.math.sci.osaka-u.ac.jp/~fujiwara

    • Related Report
      2012 Final Research Report

URL: 

Published: 2010-08-23   Modified: 2019-07-29  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi