A game-theoretic proof of Erdos-Feller-Kolmogorov-Petrowsky law of the iterated logarithm for fair-coin tossing

2014/08/08 by Takeyuki Sasai, Sasai, Takeyuki, Kenshi Miyabe +3
Computer Science · Mathematics · Physics and Astronomy · #Bayesian Modeling and Causal Inference #Probability and Statistical Research #Statistical Mechanics and Entropy #math.PR #msc:60G42

paper · pdf · doi:10.48550/arxiv.1408.1790

arxiv created 2014/11/10 · arxiv updated 2015/04/28

Abstract

We give a game-theoretic proof of the celebrated Erdos-Feller-Kolmogorov-Petrowsky law of the iterated logarithm for fair coin tossing. Our proof, based on Bayesian strategy, is explicit as many other game-theoretic proofs of the laws in probability theory.

Related

• Markov chains applied to Parrondo's paradox: The coin tossing problem
• A Feyman-Kac approach to a paper of Chung and Feller on fluctuations in the coin-tossing game
• A Markov Chain Analysis of a Pattern Matching Coin Game
• How strong can the Parrondo effect be? II
• Levy's zero-one law in game-theoretic probability