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math.PR2014★ 1 cited
A game-theoretic proof of Erdos-Feller-Kolmogorov-Petrowsky law of the iterated logarithm for fair-coin tossing
Takeyuki Sasai, Kenshi Miyabe, Akimichi Takemura
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 ex…
math.PR2012
The law of the iterated logarithm in game-theoretic probability with quadratic and stronger hedges
Kenshi Miyabe, Akimichi Takemura
We prove both the validity and the sharpness of the law of the iterated logarithm in game-theoretic probability with quadratic and stronger hedges.