Theory of prediction based on game-theoretic probability and randomness

• Project/Area Number: 25540009
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Statistical science
• Research Institution: The University of Tokyo
• Principal Investigator: Takemura Akimichi 東京大学, 情報理工学(系)研究科, 教授 (10171670)
• Co-Investigator(Kenkyū-buntansha): MIYABE Kenshi 明治大学, 理工学部, 専任講師 (00583866)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Project Status: Completed (Fiscal Year 2015)
• Budget Amount: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000); Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• Keywords: 確率論 / ランダムネス / ゲーム論的確率論 / 重複対数法則 / 脱ランダム化 / 大数法則 / 重複対数の法則

Outline of Final Research Achievements

In game-theoretic probability stochastic behavior of the players results from a game between players. However the stochastic behavior is often a consequence of a deterministic strategy of the players. In particular, the strategy of the player "Reality" does not have a counterpart in the usual measure-theoretic probability and it is a new field of research. In this project we succeeded in establishing a general method for constructing Reality's deterministic strategy.

Research Products

• [Journal Article] Derandomization in Game-Theoretic Probability (2015)
  • Author(s): Kenshi Miyabe, Akimichi Takemura
  • Journal Title: Stochastic Processes and their Applications Volume: 125 Issue: 1 Pages: 39-59
  • DOI: 10.1016/j.spa.2014.08.004
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Schnorr triviality and its equivalent notions (2015)
  • Author(s): Kenshi Miyabe
  • Journal Title: Theory of Computing Systems Volume: Volume 56, Issue 3 Pages: 465-486
  • NAID: 120005619765
  • Peer Reviewed
• [Journal Article] Unified Characterizations of Lowness Properties via Kolmogorov Complexity (2015)
  • Author(s): Kenshi Miyabe and T.Kihara
  • Journal Title: Archive for Mathematical Logic Volume: Volume 54, Issue 3 Pages: 329-358
  • Peer Reviewed
• [Journal Article] The law of the iterated logarithm in game-theoretic probability with quadratic and stronger hedges (2013)
  • Author(s): K. Miyabe and A. Takemura
  • Journal Title: Stochastic Preocesses and their Applications Volume: 123 Issue: 8 Pages: 3132-3152
  • DOI: 10.1016/j.spa.2013.03.018
  • Peer Reviewed
• [Presentation] 3ランダムネスの複雑性による特徴づけ (2015)
  • Author(s): 宮部賢志
  • Organizer: 日本数学会
  • Place of Presentation: 京都産業大学(京都府京都市）
  • Year and Date: 2015-09-16
• [Presentation] A game-theoretic proof of the Erdos-Feller-Kolmogorov-Petrowsky law of the iterated logarithm for fair-coin tossing (2014)
  • Author(s): Akimichi Takemura, Takeyuki Sasai and Kenshi Miyabe
  • Organizer: Fifth Workshop on Game-Theoretic Probability and Related Topics
  • Place of Presentation: Guanajuato （メキシコ）
  • Year and Date: 2014-11-13
• [Presentation] Derandomization in game-theoretic probability (2014)
  • Author(s): Kenshi Miyabe, Akimichi Takemura
  • Organizer: Fifth Workshop on Game-Theoretic Probability and Related Topics
  • Place of Presentation: Guanajuato （メキシコ）
  • Year and Date: 2014-11-13
• [Presentation] EFKP型の重複対数法則のゲーム論的証明 (2014)
  • Author(s): 竹村彰通，笹井健行，宮部賢志
  • Organizer: 日本数学会2014年度秋季総合分科会
  • Place of Presentation: 広島大学 （広島県，東広島市）
  • Year and Date: 2014-09-26
• [Presentation] "An introduction to game-theoretic probability from statistical viewpoint" (2013)
  • Author(s): 竹村彰通
  • Organizer: ELC Workshop on Randomness and Probability Through Computability
  • Place of Presentation: 東京大学，東京都
  • Invited
• [Remarks] 竹村彰通 研究紹介
  • URL: http://park.itc.u-tokyo.ac.jp/atstat/athp/index.html
• [Remarks] 竹村彰通 研究紹介
  • URL: http://park.itc.u-tokyo.ac.jp/atstat/athp/index.html